Should I use margin to buy a balanced fund?

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Clive
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

but I could see someone using SSO if he wanted to avoid having to manage cash very closely (regularly transferring funds between accounts, occasionally needing to wire money to the brokerage after a crash)
The aspect that concerns me about Futures/margin, is that of a glitch down spike and being stopped out at the lows only to see the price rapidly recover, leaving you out at a heavily discounted price level (nursing large realised losses).

Maintaining liquidity also limits what you can invest 'cash' in. In contrast a 50/50 SSO/bond blend can have a proportion of those bonds that will almost never be deployed to buy more stock (option to scale up to a 3x ETF further aids that), such that you can tie up some of the bonds for longer/higher yields - and longer dated bonds can have a element of inverse correlation with stocks that aids in reducing overall portfolio volatility.

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Topic Author
Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

market timer wrote:
Rob Bertram wrote:No, a fair comparison would be SSO/IEI 50/50 vs SPY/IEI 50/50.
There are three separate points in this side thread that are being combined and I think adding some confusion:

1. It is possible to replicate the returns SPY using SSO over a long horizon, paying only the borrowing costs of SSO and higher expense ratio, but without suffering from volatility drag. This is accomplished by rebalancing regularly (buying more SSO when SPY falls, selling SSO when SPY rises). Despite the fact that the ETF suffers from volatility drag over the long run, this rebalancing effectively removes it (see the paper I linked to above).
When I read the article, I struggled with the author's solution of rebalancing by bands -- averaging a rebalance every 3.8 days for a volatile period. He ignored transaction costs which will continue to erode returns. The unfortunate part of a LETF is that part of the higher ER is due to to them rebalancing the wrong way every day, and then you have to undo what they just did. As Lee pointed out, that's a lot of churn which could have a huge tax impact that we have been ignoring.
market timer wrote:2. An investor might want to pay the SSO borrowing cost and higher expense ratio (vs. SPY) if he has a way to earn a higher return elsewhere. Buying SSO takes only half the capital of buying the same notional amount of SPY, so the other half can be put into CDs, savings bonds, or as Clive suggests intermediate term bonds. In other words, the point of buying SSO is to get some implicit financing, similar to the reason one would buy futures. Johno on page 2 explains this concept in detail. Alternatively, as in this thread, the funds can be used as part of a strategy to leverage a balanced fund.
I think Johno was talking about buying an e-mini future and putting the rest in a bond/CD/FDIC insured account to offset the borrowing cost. I get that, and it's a buy and hold strategy. Price might change drastically, but the investor is still holding the target amount of the underlying asset. With an LETF, the investor holds varying amounts of the underlying asset daily, and the movement is in the wrong direction. To fix this, the investor would need to rebalance, and we get back to your point #1. Though, as soon as we say rebalance, my brain goes to the efficient frontier and the capital market line. SSO has the exact same assets as SPY, but SSO has a lower Sharpe ratio. When constructing a balanced portfolio, the smart long-term investor would pick SPY over SSO.
market timer wrote:3. SSO has the advantage over futures as a form of implicit financing in that there is no margin call risk. Futures, however, have a lower implied interest rate. Personally, I prefer futures, but I could see someone using SSO if he wanted to avoid having to manage cash very closely (regularly transferring funds between accounts, occasionally needing to wire money to the brokerage after a crash). Of course, you would have to manage the SSO fairly closely if you rebalanced often, but the consequences of failing to rebalance are less severe than one who gets a margin call and fails to add capital. In the former case, SSO implicitly reduces exposure during its own daily rebalance, in the latter, your broker may sell your securities at random, leaving you with a much more uneven exposure than you might like.
The emphasis is mine. I would argue that the opposite is true of SSO (and leveraged ETFs in general). If margin call risk is the risk of selling assets when their value drops, then SSO does that every time. (We might be arguing semantics between the differences in risk and certainty, but the outcome is the same.) We are selling assets when they go down which we want to avoid. I agree that futures would be better than SSO. Long term, I don't think that SSO has any place in a portfolio. But maybe that's just my opinion.

The daily rebalancing aspect really complicates any strategy using LETFs. I think that makes it impossible for LETFs to be treated like options and futures. With futures, you need to worry about managing cash to meet margin, with LETFs you need to balance your portfolio. On the other hand, if LETFs could track a longer period like a month or 3 months, then they might be more useful. I believe the monthly rebalanced ETFs are actually called "Long Extended ETN." SFLA looks to be leveraging the S&P 500. It doesn't seem to have much market cap, so maybe there's a problem with its implementation.
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

Much earlier in this thread, I suggested two possible books (Borrowing To Invest by Noel Whittaker and Paul Resnik, Margin Lending Explained by Paul and Jarrod Martin). Those books are difficult to get, and are introductory books. The vast majority who are writing in this thread will not benefit from reading them.

The following is a digression, but I think it is useful to the average retail investor, who wants to know more about the basics of leverage. It comes from a book "RRSP's" by Preet Banerjee. Except for one small simple chapter on leverage, it's not relevant to anyone who is not a Canadian. However, that one small chapter makes some good points.

Why do people lever? To take advantage of the fact that a lump sum contribution now will give you the lowest possible cost on your investments compared to adding money periodically as the market is going up.

The recent Bogleheads thread, with the link below, is relevant:
http://www.bogleheads.org/forum/viewtop ... 0&t=148599

Some common reasons why leverage fails:
-lack of knowledge and discipline: you should have been investing for no less than one full market cycle
-leverage at the top of a market: when one looks at mutual fund flows, they tend to go up with bull markets, and go down with bear markets; the same applies to the use of leverage
-lack of ability to meet interest costs of leverage

http://en.wikipedia.org/wiki/Federal_fu ... ical_rates

For example, Interactive Brokers charges no more than 1.58% on a margin loan at present. I believe that is 1.5% more than the present Federal Funds rate of 0.08%. However, that 0.08% is very low by historical standards. In 1982, it was around 19%, and 5% is not uncommon. Anyone using IB for margin loans must be prepared for interest rates of 6.5%. And those type of interest rates have a tendency to occur during recessions, when the stock market is doing poorly and risk of job loss is highest.

The author also recommends that those who lever have 20-40% of their portfolio in fixed income.
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

http://news.morningstar.com/articlenet/ ... ?id=665769

http://im.mstar.com/im/newhomepage/quar ... 3q2014.png

The above link gives data on the US stock market from 1988 to 2014. It divides the market into quintiles based on PE10 ratio. It relates those quintiles to the average 5 year maximum drawdown. For the cheapest quintile, the maximum drawdown is minus 5.8%; for the most expensive quintile, it's minus 28.6%.

A major reason why people buy bonds or shun leverage is the risk of stock market drawdowns. If you're using leverage, those drawdowns increase margin call risk, which converts a reversible loss into an irreversible loss. But if you own American stocks when they're cheap, the risk of such a drawdown is reduced.

The response would be that such information isn't useful right now, as the American stock market is in the second most expensive quintile, and the drawdown number for that quintile is minus 32.4%.

The cheapest quintile had a PE10 range of 12.9 to 19.7. There are quite a few other stock markets with PE10s in that range, and some which are lower.

I assume that the data from the American stock market relating PE10 to maximum drawdown applies to other markets. But I've never seen such data; has anyone else?
lee1026
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

The above link gives data on the US stock market from 1988 to 2014. It divides the market into quintiles based on PE10 ratio. It relates those quintiles to the average 5 year maximum drawdown. For the cheapest quintile, the maximum drawdown is minus 5.8%; for the most expensive quintile, it's minus 28.6%.
I am not saying that you should ignore that data, but it is based on 4 data points for each quintile. It is small enough that you can't even run a T-test to see whether it is statistically significant or not.
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

http://papers.ssrn.com/sol3/papers.cfm? ... id=2470935

The above paper links drawdown risk to CAPE, although there isn't a lot of detail given on how the data was generated.
Zb3
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Re: Should I use margin to buy a balanced fund?

Post by Zb3 »

I have found this thread very interesting. I have a similar plan myself, although my plan is ore akin to an averaging down strategy. I plan to start leveraging after a 20% drawdown in the market, and increase it the more the market drops (although leverage will increase itself by virtue of the market falling). My plan is to be able to withstand a 60% drawdown from market high on capital alone, before having to use any cash-flow from employment to top up margin. Overall the leverage levels I would use would be relatively low (although a 58% drawdown like in 08-09 would see me at around x7 leverage). I am particularly attracted to the lifecycle investing idea of diversification over time, but believe even x2 leverage can be dangerous when implemented at a market high. At x2 leverage one would be wiped out after a 50% decline (unlikely, but not uncommon). Of course, you could de lever, but thats the same as selling when the market is down, which doesn't particularly appeal to me. Selling low and buying high in order to maintain constant leverage results in volatility decay exhibited by the leveraged ETFs on the market today. I thought starting to lever once the market had already dropped would be a particularly safe way to do it,I previously intended to leverage using only Emini futures, but this thread has got me thinking that perhaps some bonds would be a good idea also. Perhaps using bonds, one could even start leveraging now where the markets are pretty overvalued. I'm in my last year of university (college in USA) so may start implementing a strategy such as yours in order to monetize my future earnings - although I would use leverage levels lower than yours, and wait for a market drawdown before increasing leverage. Hopefully I won't have to wait too long since the S&P 500 is already at a 5% drawdown from its high.

In regards to futures, I saw someone mention in this thread that their implicit financing rate was around 0.4%. It was my understanding that as futures are currently in backwardation, you are essentially being paid to leverage.

Short explanation:

The futures price is a function of dividend yields and interest rates. Where dividend yields exceed interest rates, futures will be in backwardation. Suppose you have 100k:

1) You could buy 100k of SPY or similar S&P 500 ETF which would entitle you to dividends of 2%.
2) You could put down the 5k odd margin and buy 1 Emini, and invest the remaining money at the prevailing interest rate- say 1%.

In order to make investors indifferent between the 2, the futures price must trade at a discount to the cash price. However, the closer the futures contract gets to expiry, the less interest you will earn/there will be less dividends paid out. At expiry there will be no interest or dividends to be earn --> thus cash price = futures price. The result is from buying the futures contract and holding it until expiry, you have effectively been paid to leverage.
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

From my point of view, the role of bonds in a levered stock/bond portfolio would be to decrease stock drawdown risk. An alternative to bonds is to buy value stocks.
Topic Author
Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Zb3 wrote:I have found this thread very interesting. I have a similar plan myself, although my plan is ore akin to an averaging down strategy. I plan to start leveraging after a 20% drawdown in the market, and increase it the more the market drops (although leverage will increase itself by virtue of the market falling).
Welcome to the discussion, Zb3!

Can I ask a some questions?
  • What happens if the market never drops by 20%?
  • Or what happens if the market goes up 100% before the next 20% draw down?
  • If the market drops by 60% like it did from 2007-2009 and you are now fully levered, how do you know when to get out? For example, 2011 had an 18% drop in the stock market. but ended about 2% up for the year.
  • How often are you in the market? 10% of the time?
It's hard to time the market. Smarter people than I might be able to read momentum and know when to adjust their leverage. I know that I can't.

Much earlier in the thread, Park listed a couple of articles and books to read. It seems that the prevailing belief is to leverage stocks only as that's where the reward is highest. Risk is also very high, and there's that pesky margin call. (At least, that's what I've read so far. I should probably do more reading.) My approach is unconventional in the sense that instead of leveraging a stock-only portfolio, I pick the portfolio with the highest risk-adjusted returns which has more bonds than stocks. (CAPM agrees that this is the portfolio to lever as well.) I can also pick my leverage so that the max draw down of this balanced portfolio is unlikely to trigger a margin call. That allows me to apply a buy and hold strategy.
Zb3 wrote:My plan is to be able to withstand a 60% drawdown from market high on capital alone, before having to use any cash-flow from employment to top up margin. Overall the leverage levels I would use would be relatively low (although a 58% drawdown like in 08-09 would see me at around x7 leverage).
Using a Reg T margin account, you would need to be around 1.4-1.5x levered to withstand a 58% drop. If you get in after the first 20% drop and suffer the last 38%, then you could go as much as 1.8-1.9x before getting a margin call. With a Portfolio Margin account, you could go 2.2x and get a margin call after a 38% drop.

As an extreme example, a balanced (40/60 portfolio) invested at the top of the market could go about 3.4-3.5x leverage before risking a margin call assuming a Portfolio Margin account and a similar 2007-2009 bear market. If you are investing outside the USA, there might be different margin rules in place.
Zb3 wrote:I am particularly attracted to the lifecycle investing idea of diversification over time, but believe even x2 leverage can be dangerous when implemented at a market high. At x2 leverage one would be wiped out after a 50% decline (unlikely, but not uncommon). Of course, you could de lever, but thats the same as selling when the market is down, which doesn't particularly appeal to me. Selling low and buying high in order to maintain constant leverage results in volatility decay exhibited by the leveraged ETFs on the market today.
I agree that selling to de-lever in a leveraged portfolio should only happen to avoid a margin call or when in the decumulation phase. But selling in a margin account might be part of healthy portfolio maintenance. For example, you could be tax-loss harvesting or rebalancing.

For someone in the accumulation phase of a leveraged portfolio, I invented the word "re-leveraging". It's half re-balancing so that the portfolio gets back to the target asset allocation, and it's half leveraging where money is added to the account and assets purchased so that the portfolio is back to its target leverage. Ideally, there are only purchases.
Zb3 wrote:I thought starting to lever once the market had already dropped would be a particularly safe way to do it,I previously intended to leverage using only Emini futures, but this thread has got me thinking that perhaps some bonds would be a good idea also. Perhaps using bonds, one could even start leveraging now where the markets are pretty overvalued. I'm in my last year of university (college in USA) so may start implementing a strategy such as yours in order to monetize my future earnings - although I would use leverage levels lower than yours, and wait for a market drawdown before increasing leverage. Hopefully I won't have to wait too long since the S&P 500 is already at a 5% drawdown from its high.
I don't think that there's anything safe about investing. There will always be risk, so be careful when you use the word "safe."

Well, this might be the "lump sum vs dollar cost average" argument, but I'm a firm believer that timing the market is a difficult task. Time in the market is more important. I highly recommend doing the math for yourself to see which method works best for you. I believe that buy-and-hold is a winning long-term strategy which is why I argue that a balanced portfolio should be levered, not just an all-stock portfolio. For what it's worth, this recent 5% drop might be the start of a 60% drop, or just a road bump to a 30% gain. I can't tell the future. Though, I have a strong feeling that October 2014 will be a slight dip on a chart 30 years from now.
Zb3 wrote:In regards to futures, I saw someone mention in this thread that their implicit financing rate was around 0.4%. It was my understanding that as futures are currently in backwardation, you are essentially being paid to leverage.
That is true assuming that you can find someone to pay you more than 0.4%, and there are many banks that give 0.8 - 1% rates (as you pointed out). I think it was Johno who pointed this out on page 2 of the thread.
Topic Author
Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Park wrote:http://papers.ssrn.com/sol3/papers.cfm? ... id=2470935

The above paper links drawdown risk to CAPE, although there isn't a lot of detail given on how the data was generated.
Thanks again for linking some great papers! I will try to comb the thread and put them all in a single post for easy access.
Zb3
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Re: Should I use margin to buy a balanced fund?

Post by Zb3 »

Rob Bertram wrote:Welcome to the discussion, Zb3!

Can I ask a some questions?
  • What happens if the market never drops by 20%?
  • Or what happens if the market goes up 100% before the next 20% draw down?
  • If the market drops by 60% like it did from 2007-2009 and you are now fully levered, how do you know when to get out? For example, 2011 had an 18% drop in the stock market. but ended about 2% up for the year.
  • How often are you in the market? 10% of the time?
It's hard to time the market. Smarter people than I might be able to read momentum and know when to adjust their leverage. I know that I can't.

Much earlier in the thread, Park listed a couple of articles and books to read. It seems that the prevailing belief is to leverage stocks only as that's where the reward is highest. Risk is also very high, and there's that pesky margin call. (At least, that's what I've read so far. I should probably do more reading.) My approach is unconventional in the sense that instead of leveraging a stock-only portfolio, I pick the portfolio with the highest risk-adjusted returns which has more bonds than stocks. (CAPM agrees that this is the portfolio to lever as well.) I can also pick my leverage so that the max draw down of this balanced portfolio is unlikely to trigger a margin call. That allows me to apply a buy and hold strategy.
In regards to your questions:

1) I am currently in the market and will remain in the market at x1 leverage, so if no drawdown occurs, I will not be missing out anymore than the majority of the population who do not leverage.

2) In regards to getting out of the market while it is dropping, I will not leverage past the ability of my capital level to maintain a 60% drawdown. Note that this is my capital level as the point I start leveraging, and as I will be working, I will continue contributing from my salary, so the result is I will be able to withstand a drawdown much larger than that (although that really depends when this drawdown occurs - the earlier it occurs the higher my salary will be in proportion to savings).

If I get wiped out then so be it. I'm not sure if you have read Market Timer's thread from 2007 but the basic point he makes is that everyday you are in the market you are essentially placing a wager that you will make money that day. You can do this as the odds are in your favour, but to best exploit these odds you need to place the bet as many times as you can. Basic probability suggests you will come out better off if your bet is always the same size in real terms, otherwise larger bets will dominate your payoff. The problem young people face is the older they get the more equity exposure they have in real terms. Ie for someone like me, I will have my greatest exposure to the equity market between the years of 45 to 55 (ie years 2035 to 2045). If the market does historically badly in that 10-year period, then I will have far less to retire with. The solution is to leverage while young to spread risk overtime. If I lose all my portfolio now in say a 65% drawdown (which may be around 200k), this will be nothing compared to the 45 year old who just lost 65% of his 2 million dollar portfolio. I considered leverage to withstand a 65% drawdown to be fairly safe, although I may include some bonds in my portfolio based on your idea. I'm from NZ, and the NZ dollar is relatively high at the moment in comparison to the USD, also our interest rates are very high (6% mortgage, 8% margin loan), so I was thinking of leveraging futures in the US market and using the additional cash to invest in fixed income in the NZ market. I can get 4.5% interest in a regular bank savings account over here, but I have far better options than this. I won't bore you with the details though as I doubt you are interested in the NZ market.

3) In regards to deleveraging as the market rises - the market rising will take care of this for me. I'll give you an example to illustrate, assume at the bottom of the 09 crash when the market hit 666 that i owned 2 Eminis (worth 66,600) and had 10k in my account (leverage of 6.66). At today's market level (S&P at 1900) the Eminis would be worth 190k and I would have 133,400 in my account (leverage of 1.4). Of course this would be far more cash than necessary in my futures account, so I could close one or both futures positions and invest the cash in stocks, or continue leveraging and invest the cash in bonds or at the risk free rate.

Rob Bertram wrote:Using a Reg T margin account, you would need to be around 1.4-1.5x levered to withstand a 58% drop. If you get in after the first 20% drop and suffer the last 38%, then you could go as much as 1.8-1.9x before getting a margin call. With a Portfolio Margin account, you could go 2.2x and get a margin call after a 38% drop.

As an extreme example, a balanced (40/60 portfolio) invested at the top of the market could go about 3.4-3.5x leverage before risking a margin call assuming a Portfolio Margin account and a similar 2007-2009 bear market. If you are investing outside the USA, there might be different margin rules in place.
I will not be using margin to leverage. I will be using ES futures - which allow a far greater level of leverage before a margin call is made. One ES contract currently gives exposure to 1875 x 50 = 93,750 S&P, but the maintenance margin is only 4600. As you can see it allows for a leverage of 20 before needing to top up your account.

Rob Bertram wrote:
Zb3 wrote:I am particularly attracted to the lifecycle investing idea of diversification over time, but believe even x2 leverage can be dangerous when implemented at a market high. At x2 leverage one would be wiped out after a 50% decline (unlikely, but not uncommon). Of course, you could de lever, but thats the same as selling when the market is down, which doesn't particularly appeal to me. Selling low and buying high in order to maintain constant leverage results in volatility decay exhibited by the leveraged ETFs on the market today.
I agree that selling to de-lever in a leveraged portfolio should only happen to avoid a margin call or when in the decumulation phase. But selling in a margin account might be part of healthy portfolio maintenance. For example, you could be tax-loss harvesting or rebalancing.

For someone in the accumulation phase of a leveraged portfolio, I invented the word "re-leveraging". It's half re-balancing so that the portfolio gets back to the target asset allocation, and it's half leveraging where money is added to the account and assets purchased so that the portfolio is back to its target leverage. Ideally, there are only purchases.
Zb3 wrote:I thought starting to lever once the market had already dropped would be a particularly safe way to do it,I previously intended to leverage using only Emini futures, but this thread has got me thinking that perhaps some bonds would be a good idea also. Perhaps using bonds, one could even start leveraging now where the markets are pretty overvalued. I'm in my last year of university (college in USA) so may start implementing a strategy such as yours in order to monetize my future earnings - although I would use leverage levels lower than yours, and wait for a market drawdown before increasing leverage. Hopefully I won't have to wait too long since the S&P 500 is already at a 5% drawdown from its high.
I don't think that there's anything safe about investing. There will always be risk, so be careful when you use the word "safe."

Well, this might be the "lump sum vs dollar cost average" argument, but I'm a firm believer that timing the market is a difficult task. Time in the market is more important. I highly recommend doing the math for yourself to see which method works best for you. I believe that buy-and-hold is a winning long-term strategy which is why I argue that a balanced portfolio should be levered, not just an all-stock portfolio. For what it's worth, this recent 5% drop might be the start of a 60% drop, or just a road bump to a 30% gain. I can't tell the future. Though, I have a strong feeling that October 2014 will be a slight dip on a chart 30 years from now.
I disagree that this can be characterised as timing the market. I am simply reacting to the market. I have no intention of trying to time the bottom of the market and entering at that point. I merely to take advantage of leverage when stocks are on "sale", i.e. after a 20% drop. Yes I agree there is a risk with this strategy. However, I do not seek to eliminate every risk from my life, I am merely trying to take calculated risks which I believe will pay off in the future. I am still working out the finer details of my strategy and your idea has got me thinking to incorporate some bonds into the strategy to enable me to increase the leverage.
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

http://faculty.som.yale.edu/barrynalebu ... _v2008.pdf

Another paper by Ayres and Nalebuff. I found Table Xl interesting. Results using 200% or 250% or 300% leverage were similar. I wonder whether a leverage ratio less than 200% would give similar results to those derived from a 200% leverage ratio.
Clive
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

I wonder whether a leverage ratio less than 200% would give similar results to those derived from a 200% leverage ratio.
Or how a 0.8 leverage ratio (80/20 stock/bond) compares to a 1.0 leverage ratio (100% stock),
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

Clive wrote:
I wonder whether a leverage ratio less than 200% would give similar results to those derived from a 200% leverage ratio.
Or how a 0.8 leverage ratio (80/20 stock/bond) compares to a 1.0 leverage ratio (100% stock),
http://www.mcculloch.org.nz/Documents/04_03_06.pdf

The link above relates to Clive's question, and also the question of whether to lever a stock/ bond portfolio versus a stock only portfolio. The relevant section is in the last page under the title "A surprising result". However, the analysis doesn't take into account taxes and rebalancing costs.
Clive
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Park wrote:
Clive wrote:
I wonder whether a leverage ratio less than 200% would give similar results to those derived from a 200% leverage ratio.
Or how a 0.8 leverage ratio (80/20 stock/bond) compares to a 1.0 leverage ratio (100% stock),
http://www.mcculloch.org.nz/Documents/04_03_06.pdf

The link above relates to Clive's question, and also the question of whether to lever a stock/ bond portfolio versus a stock only portfolio. The relevant section is in the last page under the title "A surprising result". However, the analysis doesn't take into account taxes.
there is a region of portfolio composition, from 55% to 100% in equities, in which the portfolio geometric return is higher than that of either of the individual
asset classes. Of course, this does not always happen – it depends on the structure of the return covariance matrix


Two assets each with 10% arithmetic yearly average, 20% standard deviation, will both tend to have 8.2% geometric (annualised gain). Where the correlation is -1 (inverse) then 50/50 of both will yield a geometric equal to the arithmetic average, 10% annualised with 0% standard deviation.
Topic Author
Rob Bertram
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Joined: Mon May 05, 2014 12:15 pm

Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Park wrote:
Clive wrote:
I wonder whether a leverage ratio less than 200% would give similar results to those derived from a 200% leverage ratio.
Or how a 0.8 leverage ratio (80/20 stock/bond) compares to a 1.0 leverage ratio (100% stock),
http://www.mcculloch.org.nz/Documents/04_03_06.pdf

The link above relates to Clive's question, and also the question of whether to lever a stock/ bond portfolio versus a stock only portfolio. The relevant section is in the last page under the title "A surprising result". However, the analysis doesn't take into account taxes and rebalancing costs.
Again, thanks for the articles!

I think that there are two very important components to Clive's question.
  1. The efficient frontier as defined by MPT is the arithmetic mean. It allows us to model what will to expect in the next near-term time period, but it does not give long-term return expectations. Geometric mean is what matters (CAGR) long-term, and standard deviation increases the spread between arithmetic and geometric mean. As you point out, the author shows that balanced portfolios can have higher expected geometric returns than an all stock portfolio due to the lower standard deviation and rebalancing (low/negative correlation).
  2. Leveraging a balanced portfolio has less call risk as its standard deviation is lower. And as just noted, the CAGR is close to or better than an all stock portfolio. I have yet to see an article compare leveraged returns of a balanced portfolio vs an all stock one. I say that people are ignoring more efficient returns by focusing only on stocks. The Ayres and Nalebuff article repeats that mistake. It's the exact same that they did in their book. They pick a final portfolio value with a specific asset allocation (say 88% stock, 12% bonds). In the accumulation phase, they want you to leverage stocks until you hit that final number, then slowly de-lever on a glide path to the asset allocation buying bonds only when leverage is gone.
lee1026
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

I'm from NZ, and the NZ dollar is relatively high at the moment in comparison to the USD, also our interest rates are very high (6% mortgage, 8% margin loan), so I was thinking of leveraging futures in the US market and using the additional cash to invest in fixed income in the NZ market. I can get 4.5% interest in a regular bank savings account over here, but I have far better options than this. I won't bore you with the details though as I doubt you are interested in the NZ market.
The good old carry trade. I won't tell you that it is a bad idea, only that you should calculate into your plans a simple "what if the US dollar gains against NZD?" The simplest way to invest in the carry trade is simply to go long on the NZD in currency futures. For example, NZD for December is trading at 0.7888, whereas it is currently at 0.7933.
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Re: Should I use margin to buy a balanced fund?

Post by Park »

Rob Bertram wrote:
Park wrote:
Clive wrote:
I wonder whether a leverage ratio less than 200% would give similar results to those derived from a 200% leverage ratio.
Or how a 0.8 leverage ratio (80/20 stock/bond) compares to a 1.0 leverage ratio (100% stock),
http://www.mcculloch.org.nz/Documents/04_03_06.pdf

The link above relates to Clive's question, and also the question of whether to lever a stock/ bond portfolio versus a stock only portfolio. The relevant section is in the last page under the title "A surprising result". However, the analysis doesn't take into account taxes and rebalancing costs.
Again, thanks for the articles!

I think that there are two very important components to Clive's question.
  1. The efficient frontier as defined by MPT is the arithmetic mean. It allows us to model what will to expect in the next near-term time period, but it does not give long-term return expectations. Geometric mean is what matters (CAGR) long-term, and standard deviation increases the spread between arithmetic and geometric mean. As you point out, the author shows that balanced portfolios can have higher expected geometric returns than an all stock portfolio due to the lower standard deviation and rebalancing (low/negative correlation).
  2. Leveraging a balanced portfolio has less call risk as its standard deviation is lower. And as just noted, the CAGR is close to or better than an all stock portfolio. I have yet to see an article compare leveraged returns of a balanced portfolio vs an all stock one. I say that people are ignoring more efficient returns by focusing only on stocks. The Ayres and Nalebuff article repeats that mistake. It's the exact same that they did in their book. They pick a final portfolio value with a specific asset allocation (say 88% stock, 12% bonds). In the accumulation phase, they want you to leverage stocks until you hit that final number, then slowly de-lever on a glide path to the asset allocation buying bonds only when leverage is gone.
What are advantages to levering a stock/bond portfolio, as opposed to a stock only portfolio?

It decreases drawdown risk. But a simpler way to decrease drawdown risk is to decrease leverage. A fact that isn't mentioned frequently is that a 100% stock portfolio has a high degree of leverage. When ones looks at the ratio of total liabilities to total assets of American stocks, it's approximately 50%. I have heard Ray Dalio in an interview state, that if you remove the leverage already in stocks, the returns and volatility of stocks become more like bonds. I haven't seen the data on that though.

It diversifies risk premia.

You can get the credit risk premium by bond investing, and it doesn't correlate well with the equity risk premium. However, in market drawdowns, the correlation between the two increases considerably. And that's just when you don't want it to.

You can get the term risk premium by bond investing, and once again, it doesn't correlate well with the equity risk premium. At present, the 10 year Treasury has a yield of 2.42%, and the 30 has a yield of 3.12%. You can borrow money at IB for 1.59%, and futures would have a lower rate yet. So you are making money doing this, although the historical difference between stocks and the call money rate is around 4%.

In a flight to quality (2008), stocks go down and government bonds go up, with long term bonds going up more than short term bonds. So levering a balanced portfolio works well then.

If interest rates go down, the return from levering a bond portfolio would increase. But I think the probability of rates staying the same or going up is higher. If rates go up, this may not turn out well (see Tables 2 and 3 of this link http://servowealth.com/resources/articl ... your-bonds ).

When the yield curve inverts, this may also not turn out well. Long term rates won't be higher than short term rates, and your stocks will simultaneously be tanking.

One of the downsides of levering a stock/bond portfolio is the increased rebalancing costs, although that may be insignificant. But another downside is the decreased tax arbitrage. This will of course depend on one's tax laws. For me, it's possible to have a negative pretax return on levered stocks, but come out ahead on a posttax basis. That's not possible with bonds.

"I have yet to see an article compare leveraged returns of a balanced portfolio vs an all stock one."

I agree with the above statement. And until I do, I'm reluctant to lever a stock/bond portfolio. MPT is not new. If levering a stock/ bond portfolio was better than levering a stock only portfolio, wouldn't someone have addressed this question earlier?

"As you point out, the author shows that balanced portfolios can have higher expected geometric returns than an all stock portfolio due to the lower standard deviation and rebalancing (low/negative correlation)"

I agree that the author states that such a portfolio can have a higher expected geometric return; however, he doesn't say that it will.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Park wrote:You can get the term risk premium by bond investing, and once again, it doesn't correlate well with the equity risk premium.
Depends what you mean by "doesn't correlate well". The long-term correlation of 10-year T bonds and S&P500 (1928-2013) is -0.03. This is the same as the long-term correlation between S&P 500 and 3-month T bills. Pretty close to 0.
Park wrote:At present, the 10 year Treasury has a yield of 2.42%, and the 30 has a yield of 3.12%. You can borrow money at IB for 1.59%, and futures would have a lower rate yet. So you are making money doing this <snip>
You don't know if you are making money or not. You can only know whether or not you made money in the past. You will make money unless the yield curve moves too far against you, in which case you will lose money.
Park wrote:In a flight to quality (2008), stocks go down and government bonds go up, with long term bonds going up more than short term bonds.
Sometimes, perhaps even more often than not, but not always. Not in 1931. Below are the returns for S&P 500, 3-month T bills, and 10-year T bonds respectively:

1931 -43.84% 2.31% -2.56%

Source: http://www.stern.nyu.edu/~adamodar/pc/d ... tretSP.xls

Kevin
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Re: Should I use margin to buy a balanced fund?

Post by Zb3 »

lee1026 wrote:
I'm from NZ, and the NZ dollar is relatively high at the moment in comparison to the USD, also our interest rates are very high (6% mortgage, 8% margin loan), so I was thinking of leveraging futures in the US market and using the additional cash to invest in fixed income in the NZ market. I can get 4.5% interest in a regular bank savings account over here, but I have far better options than this. I won't bore you with the details though as I doubt you are interested in the NZ market.
The good old carry trade. I won't tell you that it is a bad idea, only that you should calculate into your plans a simple "what if the US dollar gains against NZD?" The simplest way to invest in the carry trade is simply to go long on the NZD in currency futures. For example, NZD for December is trading at 0.7888, whereas it is currently at 0.7933.

I'm not interested in currency investment specifically, I'm just attracted to NZ's higher fixed income returns and the currency gain would be a bonus. Currency trading is a zero sum game, whereas stock index futures aren't if you always go long since stocks trend upwards. I noticed earlier in the thread you posted that the implied interest rate in Emini futures is 0.4%, I was wondering if you know how that was calculated? Is it the opportunity cost of the money in your futures account? Since futures are currently in backwardation, if you hold until expiry you are getting paid a premium above cash price.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Thanks again for your insight and contribution to the discussion, Park!
Park wrote:What are advantages to levering a stock/bond portfolio, as opposed to a stock only portfolio?
It decreases drawdown risk. But a simpler way to decrease drawdown risk is to decrease leverage. <snip> It diversifies risk premia.
Those are both true, but a simpler answer is that a balanced portfolio has a higher Sharpe ratio. It's more efficient, so we get better returns for our target risk. And as you say, max draw (call risk) is important as that is when an unrealized loss becomes realized. It essentially creates an upper ceiling to the leverage that can be applied to the portfolio. You are correct that lowering leverage also lowers call risk, but it also lowers expected returns. (Also, lower volatility reduces the drag on CAGR while doing nothing to average returns. CAGR is what matters in the end.)
Park wrote:A fact that isn't mentioned frequently is that a 100% stock portfolio has a high degree of leverage. When ones looks at the ratio of total liabilities to total assets of American stocks, it's approximately 50%. I have heard Ray Dalio in an interview state, that if you remove the leverage already in stocks, the returns and volatility of stocks become more like bonds. I haven't seen the data on that though.
I might be oversimplifying the total stock market. The mathematician in me wants to treat it as a single asset with a mean and variance that captures all of the different things that companies do. I am assuming a moderately efficient market where all of a company's leverage and risk is captured in their stock price which gets aggregated into the total market.
Park wrote:One of the downsides of levering a stock/bond portfolio is the increased rebalancing costs, although that may be insignificant. But another downside is the decreased tax arbitrage. This will of course depend on one's tax laws. For me, it's possible to have a negative pretax return on levered stocks, but come out ahead on a posttax basis. That's not possible with bonds.
For someone in the accumulation or decumulation phase, rebalancing can happen on the deposits/withdraws. As you say, they are insignificant. You are correct; taxes are significant and cannot be ignored. The margin interest should offset most of the bond yield, so there is maybe 1-2% coming from bonds that are fully taxed. I probably need to continue this experiment for a year or two in order to get a better understanding of managing taxes.
Park wrote:
Rob Bertram wrote:I have yet to see an article compare leveraged returns of a balanced portfolio vs an all stock one."
I agree with the above statement. And until I do, I'm reluctant to lever a stock/bond portfolio. MPT is not new. If levering a stock/ bond portfolio was better than levering a stock only portfolio, wouldn't someone have addressed this question earlier?
That's exactly what I was hoping when I started this topic -- that there would be an obvious reason why one should not leverage a balanced portfolio. There doesn't seem to be an obvious reason. On the other hand, we have tools like CAPM and the Capital Market Line that address leveraging a portfolio. To me, it seems like a simple application of CAPM to an investing universe of stocks and bonds. I believe that there is strong agreement in the community that a balanced stock/bond portfolio is more efficient than an all stock portfolio.

And buy-and-hold might not be the optimal way to get the best returns. There are probably better methods to look at market factors/momentum/valuations and adjust leverage accordingly for higher returns. From all the reports I've seen, indexing beats about 80-90% of actively managed funds. However, that means there are 10-20% that beat indexing. I imagine from a complexity and investing standpoint, buy-and-hold is a fairly boring strategy. Adding bonds to the strategy probably makes it more boring. People wanting to increase returns probably dismiss the boring stuff. This might be a situation where the quest for a perfect strategy is the enemy of a good strategy.

Leverage might also be a relatively new possibility for the retail investor. Futures have been around for a while, but the contract size is prohibitively large for small (retail) traders. The e-minis are better, but they were introduced in the late '90s/early 2000s. For a retail investor who maybe contributes $5-6k/year, ETFs would need to fill the gap to maintain a target leverage ratio. ETFs are also relatively new. I believe that BND (Vanguard's Total Bond Market) was released in 2008. Portfolio margin accounts also were introduced around that time as well.
Park wrote:
Rob Bertram wrote:As you point out, the author shows that balanced portfolios can have higher expected geometric returns than an all stock portfolio due to the lower standard deviation and rebalancing (low/negative correlation)
I agree that the author states that such a portfolio can have a higher expected geometric return; however, he doesn't say that it will.
Well, nobody can predict the future. We can only set mean/variance expectations. But things like expected average returns vs geometric returns can be expressed mathematically. I believe that the difference can be approximated: (geo ret) = (avg ret) - 0.5 *(std dev)^2. Though, I don't remember where I read that. That should give us enough tools to allow us to compare the CAGR of a balanced portfolio to an all-stock portfolio.
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Re: Should I use margin to buy a balanced fund?

Post by Park »

In a tax advantaged account, one way to get leverage is use deep in the money (DITM) calls. I've considered a strategy of buying 2 year DITM calls, and rolling them after one year. But I came to the conclusion that the only ETF where this could work was SPY; bid ask spread on other ETFs decreased the chance of a positive return considerably. And at present, one runs the risk of early exercise with deep in the money calls (dividend greater than sum of interest and cost of put at same strike price).

Comments, including criticisms, are most welcome.
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Re: Should I use margin to buy a balanced fund?

Post by Beliavsky »

Park wrote:In a tax advantaged account, one way to get leverage is use deep in the money (DITM) calls. I've considered a strategy of buying 2 year DITM calls, and rolling them after one year. But I came to the conclusion that the only ETF where this could work was SPY; bid ask spread on other ETFs decreased the chance of a positive return considerably. And at present, one runs the risk of early exercise with deep in the money calls (dividend greater than sum of interest and cost of put at same strike price).
If you own the calls, you choose when to exercise them. Also note that options on the SPX index itself are European and do not have the early exercise feature.
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Re: Should I use margin to buy a balanced fund?

Post by Bogle101 »

This is a great idea. Margin always makes sense.

Unless you need to tap these funds sooner than a long term timeframe.

Or if there is a protracted bear market, which compounds the interest you pay on those down years.

Or you have a life emergency and your cash flow dries up.

So basically, as long as you start this endeavour in a solid bull market, don't have a life emergency and can always stay the course no matter what, this is a can't miss plan!
40% Extended Market | 40% S&P 500 | 10% REIT | 5% State Muni Bond | 5% Cash
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Re: Should I use margin to buy a balanced fund?

Post by market timer »

Park wrote:In a tax advantaged account, one way to get leverage is use deep in the money (DITM) calls. I've considered a strategy of buying 2 year DITM calls, and rolling them after one year. But I came to the conclusion that the only ETF where this could work was SPY; bid ask spread on other ETFs decreased the chance of a positive return considerably. And at present, one runs the risk of early exercise with deep in the money calls (dividend greater than sum of interest and cost of put at same strike price).

Comments, including criticisms, are most welcome.
I think early exercise complicates the liquidity problems of SPY LEAPS. Of course, you can choose not to exercise early, but this means you're leaving money on the table. The effect is that the effective expiration date is not the listed expiration date, but sometime earlier.

Rather than deal with the higher transaction costs of buying and selling LEAPS, I'd rather use futures, which are allowed in an IRA. If futures are not available, due to account permissions, I think the next best solution is to buy leveraged ETFs and rebalance periodically.
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Re: Should I use margin to buy a balanced fund?

Post by abuss368 »

Bogleheads have found it to be an important investment principle not to invest of margin. In fact, Jack Bogle has often advised not to invest on margin in many of his interviews and excellent books.

We would be well to follow Mr. Bogle's advice.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

market timer wrote:
Park wrote:In a tax advantaged account, one way to get leverage is use deep in the money (DITM) calls. I've considered a strategy of buying 2 year DITM calls, and rolling them after one year. But I came to the conclusion that the only ETF where this could work was SPY; bid ask spread on other ETFs decreased the chance of a positive return considerably. And at present, one runs the risk of early exercise with deep in the money calls (dividend greater than sum of interest and cost of put at same strike price).

Comments, including criticisms, are most welcome.
I think early exercise complicates the liquidity problems of SPY LEAPS. Of course, you can choose not to exercise early, but this means you're leaving money on the table. The effect is that the effective expiration date is not the listed expiration date, but sometime earlier.

Rather than deal with the higher transaction costs of buying and selling LEAPS, I'd rather use futures, which are allowed in an IRA. If futures are not available, due to account permissions, I think the next best solution is to buy leveraged ETFs and rebalance periodically.
Ayres and Nalebuff suggest using S&P 500 LEAPS to get 2x leverage in their book. It is in line with a buy-and-hold strategy. Futures might be the best way to get bond leverage. I agree with Market Timer that futures combined with regular ETFs seem to be the better tools. Though, you'll have to roll your futures four times a year. What complicates matters is that some brokers do not allow futures in an IRA, so the strategy might be broker specific. Yet, I believe that it's possible that one could manage a 40/60 portfolio leveraged 2-3x in an IRA. We still have the problem of large contract sizes.

I'm not convinced that leveraged ETFs have a place in a buy-and-hold portfolio. The need to frequently rebalance makes them problematic in my opinion. Though, maybe it's more personal disappointment with how leveraged ETFs work.
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Re: Should I use margin to buy a balanced fund?

Post by Park »

Beliavsky wrote:
Park wrote:In a tax advantaged account, one way to get leverage is use deep in the money (DITM) calls. I've considered a strategy of buying 2 year DITM calls, and rolling them after one year. But I came to the conclusion that the only ETF where this could work was SPY; bid ask spread on other ETFs decreased the chance of a positive return considerably. And at present, one runs the risk of early exercise with deep in the money calls (dividend greater than sum of interest and cost of put at same strike price).
If you own the calls, you choose when to exercise them. Also note that options on the SPX index itself are European and do not have the early exercise feature.
Your point on SPX is well taken. But it's still the S&P500, and at present valuations, I don't want to lever the S&P500.

About owning calls and choosing when to exercise them, you can buy a 2 year DITM call that is priced on the basis of early exercise and choose not to exercise it. But that means your effective interest rate has increased due to the dividend that you have forgone.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Rob Bertram wrote:I'm not convinced that leveraged ETFs have a place in a buy-and-hold portfolio. The need to frequently rebalance makes them problematic in my opinion. Though, maybe it's more personal disappointment with how leveraged ETFs work.
Rob, half in 2x S&P500 (SSO), half in a VFISX/TLT (shorter dated/longer dated bond) barbell (to compensate (and more) for what the LETF pays to borrow) and yearly gains of the individuals (total gains) :

Year TLT VFISX SSO SPY
2007 10.3 7.9 1 5.1
2008 33.9 6.7 -67.9 -36.8
2009 -21.8 1.4 47.3 26.4
2010 9 2.6 26.8 15.1
2011 34 2.3 -2.9 1.9
2012 2.6 0.6 31 16
2013 -13.4 -0.1 70.5 32.3
YTD Oct 20.1 0.8 12.2 7

Rebalancing once/year back to 50/25/25 SSO/TLT/VFISX and you would have had some assets losing to help offset other assets gains/profit-takes (reduce tax liabilities).

From January 2007 through to recent, SPY (100%) +61.7% total gain (6.3% annualised), compared to the above 50/25/25 blend (yearly rebalanced) +102.8% (9.4% annualised).

Yearly % total gains

SPY SSO/(TLT/VFISX)
5.1 5.1
-36.8 -23.8
26.4 18.5
15.1 16.3
1.9 7.6
16 16.3
32.3 31.9
7 11.3

Image

If you wanted to leverage a 50/50 stock/bond blend to 66/66 then 33% 2x stock ETF, 67% bonds. To leverage to 75/75 stock/bond then 25% 3x stock, 75% bonds.

[Also remember there are three options when it comes to rebalancing. If your bonds are tied up for a term (locked in/penalty for early withdrawal) and you need to add more stock exposure, then if you have $50K of stock exposure and are holding that via £25K in 2x, and want to increase to $55K stock exposure, then you might sell $5K of 2x and buy $5K of 3x. The other two options being to sell either shorter dated or longer dated bonds to buy more stock when there's no lock-in/penalty - ideally choosing whichever is the more appropriate choice at the time i.e. if long dated bonds had moved strongly positive as stocks declined as occurred in 2008, then reducing/profit taking long dated bonds is likely the more appropriate choice.]
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

Park wrote:
Beliavsky wrote:
Park wrote:In a tax advantaged account, one way to get leverage is use deep in the money (DITM) calls. I've considered a strategy of buying 2 year DITM calls, and rolling them after one year. But I came to the conclusion that the only ETF where this could work was SPY; bid ask spread on other ETFs decreased the chance of a positive return considerably. And at present, one runs the risk of early exercise with deep in the money calls (dividend greater than sum of interest and cost of put at same strike price).
If you own the calls, you choose when to exercise them. Also note that options on the SPX index itself are European and do not have the early exercise feature.
Your point on SPX is well taken. But it's still the S&P500, and at present valuations, I don't want to lever the S&P500.

About owning calls and choosing when to exercise them, you can buy a 2 year DITM call that is priced on the basis of early exercise and choose not to exercise it. But that means your effective interest rate has increased due to the dividend that you have forgone.
Well, what do you want to lever?
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Re: Should I use margin to buy a balanced fund?

Post by Day9 »

lee1026 wrote:
Park wrote:
Beliavsky wrote: Your point on SPX is well taken. But it's still the S&P500, and at present valuations, I don't want to lever the S&P500.
...
Well, what do you want to lever?
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45% Long term Treasuries (25+ year maturity)
25% Emerging markets equities
20% Developed markets equities (ex-US)
30% Precious metals
-20% Cash

Note he holds no US stocks. Long term treasuries are up something like 25% YTD so he must be doing well.
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Re: Should I use margin to buy a balanced fund?

Post by Park »

http://ddnum.com/articles/leveragedETFs.php

About the above link, I'm not certain that I agree with all the points raised about leveraged ETFs, but some good points about leverage in general are made.

Volatility drag is the difference between arithmetic and geometric returns. For example, if an index goes up 10% one day and then goes down 10% the next day, the arithmetic return is 0. However, the geometric return, which is what you care about, is minus 1%.

Volatility drag = 0.5 times (volatility squared): volatility is the standard deviation of return.

If you lever two times, return will double, but volatility drag will go up four times. If you lever enough, the volatility drag will overwhelm the increased return. So there is a limit as to how much leverage can increase returns.

For most stock markets, that limit is a leverage ratio of around 2, but it depends on the market. For example, the above link found that optimal leverage on the S&P500 from 1950 to 2009 was around 3. And more relevant to present investors, it found that the optimal leverage ratio for the Nikkei 225 from 1984 to 2009 was 0.5.

IN 1950, the PE10 of the S&P500 was around 10.

http://www.multpl.com/shiller-pe/

In 1984, the PE10 of the Nikkei 225 was around 32.

http://www.vectorgrader.com/indicators/ ... e-earnings
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Re: Should I use margin to buy a balanced fund?

Post by Park »

Upthread, I gave a link about leveraged ETFs, and how one might be able to use them by rebalancing; I give the link again below.

http://ieor.columbia.edu/files/seasieor ... v_2009.pdf


Here are two more links about using rebalancing to hold leveraged ETFs for more than one day:

http://ieor.columbia.edu/files/seasieor ... v_2009.pdf
https://www.math.nyu.edu/faculty/avella ... 090515.pdf

The first of the two links is practical, and goes into more depth about rebalancing. Of the three above links, the first two are publications that originate in Proshares, a distributor of leveraged ETFs. The last link is from authors who don't look like they have a relationship to the industry, and who provide a rigorous academic analysis.

I'm not encouraging people to use leveraged ETFs or leverage in general. In one of the links I have previously given, the author stated that no more than 10% of investors should use leverage, and I would tend to agree with that. But leverage is a reasonable option for an experienced investor to consider. And in a tax advantaged account, LETFs may be one of the few ways to obtain leverage. If you are going to use leverage, it is important to exercise due diligence.
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Re: Should I use margin to buy a balanced fund?

Post by market timer »

Rob Bertram wrote:Ayres and Nalebuff suggest using S&P 500 LEAPS to get 2x leverage in their book.
Recently, the combination of low volatility and low interest rates has led to historically low time premia on call options. This has given rise to the early exercise complication on LEAPS that Park mentions. There simply isn't a market in many LEAPS because of this--after all, why would an investor buy an illiquid LEAPS that is expected to be exercised in two months rather than a more liquid two-month option? After the Fed hikes short term interest rates, this problem should go away. LEAPS have many good attributes from a buy-and-hold perspective--eligible for long term cap gains tax treatment, no risk of margin call, and implied borrowing costs near the risk-free rate.
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Re: Should I use margin to buy a balanced fund?

Post by Park »

http://seekingalpha.com/article/147312- ... -etfs-work

For the sake of completeness, here is another link on rebalancing with this type of ETF. This rebalancing will most likely result in cap gains, and make leveraged ETFs less feasible in a taxable account.
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Re: Should I use margin to buy a balanced fund?

Post by Johno »

Zb3 wrote: I noticed earlier in the thread you posted that the implied interest rate in Emini futures is 0.4%, I was wondering if you know how that was calculated? Is it the opportunity cost of the money in your futures account? Since futures are currently in backwardation, if you hold until expiry you are getting paid a premium above cash price.
Backwardation/contango is not really a meaningful concept for financial futures, where the underlying can be basically frictionessly arbitraged against the futures, long or short, without considerations like storage cost, perishability and so forth that apply to various physical commodities. The ES contract trades at a premium/discount to the cash SP index by strictly the difference between the dividend payout rate on the index and the market clearing rate at which market participants can finance a position in the cash index (basket of stocks representing the whole S&P). And therefore the total return of a long position in the contract will be the same as a position in the underlying basket if financed at the same rate (there's no potential for a particular advantage/disadvantage in return just because the contract is at premium/discount to cash, so again unlike commodity futures). We might assume that the rate would be LIBOR since large institutions are dominant in the market and finance at around that rate. But instead we can take the known futures and cash prices and (basically, for such a short period) dividends and back out the implied financing rate, where it turns out recently to be somewhat above (USD) LIBOR for 3 or less month term, ie around 0.4%. The CME calculates and releases this daily.

However, it's pretty far below the rate at which individuals can invest in govt gteed deposits, which is around .95%, so there's a worthwhile arbitrage to hold net non-leveraged stock positions in an IRA (less so and more complicated at the least in taxable accounts) in ES contracts and bank accounts rather than S&P ETF's.

The caveat is mainly the issue of maintaining liquidity in the futures account, ie not getting kicked out of the position on a short term dip in the market, and cash in the futures account wouldn't get any interest (Interactive Brokers pays Fed Funds -.5% min zero IIRC). However as also previously noted this is not a completely open ended risk to the extent of any temporary market disruption one might imagine. The daily movement of the contract and hence margin call is limited to 20%, after which trading is halted till the following day. The strategy can be pursued with around 75% of the money in the bank account as long as the investor is ready to wire money from the bank account to futures account in case of a huge down day, before trading resumes the next day.

Also to get a little more fancy the investor could have some of the 25% in the futures account in say a short term corp bond ETF with a conditional sell order triggered by a drop in the ES big enough to need the extra margin. Then it's neither a literal arbitrage or really zero net leverage, since some extra duration and credit risk is being taken on the short term bond ETF. And this variation could be carried further to moderate risk leverage on the whole amount: ES contract exposure on 100% of notional, cash for just in excess of maintenance margin requirement (5% roughly) and short term bond ETF for 95%, with conditional sell orders on the bond ETF indexed to the ES contract to meet margin calls if the ES drops.
Clive
Posts: 1950
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Park PM'd me asking me to drop in a comment here ... so :

Broadly stocks are similar to leveraged bonds. A typical/average stock has a debt/equity ratio of 1. Compare 50/50 stock/T-Bill to total bond and http://www.portfoliovisualizer.com/back ... peration=0

Go to etfreplay.com select the BACKTESTING, ETF PORTFOLIO drop down and plug in 75% UST, 25% UDOW (3x bonds, 3x stocks) and test .... and you'll see the results of a leveraged balanced fund type asset allocation.

Don't expect leveraged ETF's to provide multiples of the gains (losses), broadly they just provide the same gain as 1x - its the volatility that LETF's scale up (somewhat like high beta stocks).

Investors can make gains out of price appreciation, income (dividends, interest), and/or volatility capture. Generally they're all as equally as rewarding, price appreciation = dividends = interest = volatility/rebalance trading gains = inflation. Stocks provide exposure to two of those, price appreciation and dividends all wrapped up into one. Similar in some respects to how foreign bonds provide exposure to bond total gain +/- FX gain/loss.

You don't need to rebalance LETF's that often. 50% SSO (2x S&P500), 50% IEI (bonds) and compare that to 100% SPY over a 12 month long period (etfreplay again can help visualise that) and the 'tracking error' is relatively small. i.e. rebalancing once/year is OK. When the 50% bonds relatively outperforms the cost of the 50% amount that the LETF in effect (conceptually) borrows to gain leveraged exposure then you get to pocket the difference.

Park, many are strongly opposed to LETF's. Often they'll be accepting to holding stocks that might have high levels of debt/equity, high beta .... but can't or wont connect that with how LETF's can replicate similar in a productive manner in practice. Math will typically be used to 'prove' their reasoning of LETF's failings. In some cases that's justified, such as commodity or short LETF's, but in other cases its not. Personally I use LETF's extensively to good effect in practice, buying and holding (with periodic rebalancing) for years. Prior to that I used to try and pick stocks, now its more a case of hold broad stock exposure and focus efforts on improving bond rewards whilst striving to minimise bond risks.
Topic Author
Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Park wrote:http://ddnum.com/articles/leveragedETFs.php

About the above link, I'm not certain that I agree with all the points raised about leveraged ETFs, but some good points about leverage in general are made.
Thanks for the awesome discussion, Park!

I like that the Author takes a look into geometric mean/CAGR. I wanted to hear everyone's thoughts on CAGR of a leveraged portfolio. Though, a better crafted post might have to wait. I'm in the process of moving. Most of my stuff is in boxes, and I haven't re-assembled my office yet. My apologies for the incomplete thoughts.

Compound annual growth rate (CAGR) / geometric mean is a very important measure that we only know after the fact. MPT uses arithmetic mean and standard deviation, but the article you posted gives an approximation for calculating expected CAGR from arithmetic mean and standard deviation.

Anyway, here are my thoughts on CAGR: A long-term, buy-and-hold portfolio that we are discussing, has a different CAGR from we would expect from the expected arithmetic mean and standard deviation. There are two expected returns and standard deviations to consider. First, there is the fully leveraged portfolio that consists of your money and the borrowed broker's money. Let's say that it's a 40/60 balanced portfolio. This has the expected returns of any regular (unleveraged) 40/60 portfolio minus slightly higher expenses due to margin loan. And the CAGR is roughly the arithmetic mean minus half the volatility squared. Second, we have the capital that we have invested in the portfolio. The the expected arithmetic mean and standard deviations will be scaled by leverage. The CAGR, however, looks like it scales linearly similar to the arithmetic mean with leverage.

Leveraged ETFs do seem to be a reasonable option for tax-advantaged accounts that cannot use margin directly despite my earlier objections. Most of the articles seem to suggest that managing a portfolio of LETFs needs to be rebalanced frequently to exploit the volatility -- rebalanced monthly if not weekly. The transaction costs might be acceptable within a certain range of tracking error. Maybe I just don't like SSO. UPRO (3x S&P 500) looks to be useful combined with UST (2x 7-10 yr treasuries). The only 3x bond ETFs look to be 20-year treasuries. If there are others, I haven't found them.
lee1026
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

Futures are permitted for IRAs, and one can easily deploy massive leverage that way.
Zb3
Posts: 71
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Re: Should I use margin to buy a balanced fund?

Post by Zb3 »

Johno wrote: Backwardation/contango is not really a meaningful concept for financial futures, where the underlying can be basically frictionessly arbitraged against the futures, long or short, without considerations like storage cost, perishability and so forth that apply to various physical commodities. The ES contract trades at a premium/discount to the cash SP index by strictly the difference between the dividend payout rate on the index and the market clearing rate at which market participants can finance a position in the cash index (basket of stocks representing the whole S&P). And therefore the total return of a long position in the contract will be the same as a position in the underlying basket if financed at the same rate (there's no potential for a particular advantage/disadvantage in return just because the contract is at premium/discount to cash, so again unlike commodity futures). We might assume that the rate would be LIBOR since large institutions are dominant in the market and finance at around that rate. But instead we can take the known futures and cash prices and (basically, for such a short period) dividends and back out the implied financing rate, where it turns out recently to be somewhat above (USD) LIBOR for 3 or less month term, ie around 0.4%. The CME calculates and releases this daily.
Thanks for the reply. I thought backwardation referred to when the cost of carry was positive - i.e. where the contract trades under the spot price but converges with the spot price at expiry. This is based on the cost to buy and carry until term an equity portfolio based on the underlying index (i.e. SPY for an S&P Emini) - which is a function of dividends and interest rates?

I'm still slightly confused about the implied financing rate. I had a look online but couldn't really find much on it apart from a formula on the CME website. It seemed to me that the implied finance occurrs when the contract is rolled over, although conceptually I don't understand the reason behind the numbers in the formula. I don't understand why there is a financing rate in a futures contract since you are not technically borrowing anything - you are only required to have enough to cover the change in the underlying index, not buy the value of the index itself at expiry.

If the implied financing rate is 0.4% per quarter why would people buy futures contracts at all when they could lend on margin from IB at 1.59%. Also why would people buy a futures contract at invest the rest in the bank at .95% when yearly futures interest costs would be 1.6%? Or is this 0.4% annualised and not a quarterly interest cost?



Johno wrote:Also to get a little more fancy the investor could have some of the 25% in the futures account in say a short term corp bond ETF with a conditional sell order triggered by a drop in the ES big enough to need the extra margin. Then it's neither a literal arbitrage or really zero net leverage, since some extra duration and credit risk is being taken on the short term bond ETF. And this variation could be carried further to moderate risk leverage on the whole amount: ES contract exposure on 100% of notional, cash for just in excess of maintenance margin requirement (5% roughly) and short term bond ETF for 95%, with conditional sell orders on the bond ETF indexed to the ES contract to meet margin calls if the ES drops.
This is an interesting idea. Would Interactive Brokers offer this kind of service?
Zb3
Posts: 71
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Re: Should I use margin to buy a balanced fund?

Post by Zb3 »

Park wrote:Upthread, I gave a link about leveraged ETFs, and how one might be able to use them by rebalancing; I give the link again below.

http://ieor.columbia.edu/files/seasieor ... v_2009.pdf


Here are two more links about using rebalancing to hold leveraged ETFs for more than one day:

http://ieor.columbia.edu/files/seasieor ... v_2009.pdf
https://www.math.nyu.edu/faculty/avella ... 090515.pdf

The first of the two links is practical, and goes into more depth about rebalancing. Of the three above links, the first two are publications that originate in Proshares, a distributor of leveraged ETFs. The last link is from authors who don't look like they have a relationship to the industry, and who provide a rigorous academic analysis.

I'm not encouraging people to use leveraged ETFs or leverage in general. In one of the links I have previously given, the author stated that no more than 10% of investors should use leverage, and I would tend to agree with that. But leverage is a reasonable option for an experienced investor to consider. And in a tax advantaged account, LETFs may be one of the few ways to obtain leverage. If you are going to use leverage, it is important to exercise due diligence.
Those links were very interesting and have started to change my perspective on leveraged ETFs. I suppose the only drawback of using them for leverage is the financing rate is higher than other methods - i.e. most LETFS have an expense ratio around 0.9%. I suppose with LETFs you can't be margin called. As they maintain constant leverage a 33% drop in the index wouldn't wipe out a x3 leveraged ETF, but something about selling excessively as the market drops just seems inherently wrong. I would really like to see how a x3 LETF would have performed in 2008 but etfreplay can't go back that far. Although I did look at SSO in 2008 and it surprised me that it went down less than double the index, I would have thought that volatility decay would have resulted in SSO dropping more than double the index.
Topic Author
Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

lee1026 wrote:Futures are permitted for IRAs, and one can easily deploy massive leverage that way.
Sadly, it depends on the broker. For example, Vanguard allows options but not futures. Fidelity and Schwab don't allow futures trading in an IRA, either. Those seem to be some of the popular retirement custodians on this forum due to their low-cost index funds. http://sixfigureinvesting.com/2012/11/t ... in-an-ira/

They all allow stocks and ETFs, so leveraged ETFs might be an acceptable choice. But I agree that futures allow better control of leverage.
Tanelorn
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Re: Should I use margin to buy a balanced fund?

Post by Tanelorn »

Zb3 wrote:
Johno wrote:Also to get a little more fancy the investor could have some of the 25% in the futures account in say a short term corp bond ETF with a conditional sell order triggered by a drop in the ES big enough to need the extra margin. Then it's neither a literal arbitrage or really zero net leverage, since some extra duration and credit risk is being taken on the short term bond ETF. And this variation could be carried further to moderate risk leverage on the whole amount: ES contract exposure on 100% of notional, cash for just in excess of maintenance margin requirement (5% roughly) and short term bond ETF for 95%, with conditional sell orders on the bond ETF indexed to the ES contract to meet margin calls if the ES drops.
This is an interesting idea. Would Interactive Brokers offer this kind of service?
You wouldn't need a service, or even set a conditional sell order (which would need to be re-set as the market prices move around). If your plan is to sell the fixed income ETF if there's a margin call, you can set their "liquidate last" flag on all your other positions and then do nothing. If there's a problem, their system would sell enough of that one first. I don't know what it would do after that if you have multiple other positions - probably sell ES since it's the most liquid one, but I'm not sure.
Clive
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Rob Bertram wrote:Leveraged ETFs do seem to be a reasonable option for tax-advantaged accounts that cannot use margin directly despite my earlier objections. Most of the articles seem to suggest that managing a portfolio of LETFs needs to be rebalanced frequently to exploit the volatility -- rebalanced monthly if not weekly. The transaction costs might be acceptable within a certain range of tracking error. Maybe I just don't like SSO. UPRO (3x S&P 500) looks to be useful combined with UST (2x 7-10 yr treasuries).
To give a example, I use (being a Brit) 2MCL a 2x FT250 (UK mid cap, which in the scale of US stock sizes might be considered as small cap), 25% weighted, 3USL (Russell 1000 3x) 16.6% weighted, and the rest in VGOV (UK bond ETF). That's comparable to holding 50% US stock 50% UK 'small' cap stocks.

Since July 2013 3USL is up 77% by itself, compared to the S&P500 total return being up 25% (rounding figures US$ based gains (68% and 18% gains in GB£ terms respectively)). I don't have the exact Russell 1000 gain over the same period, but it was pretty similar to the S&P500 total return. i.e. US stocks have generally been in a uptrend since July 2013 and to note is that the 3x more or less provided three times the 1x total gain reward all by itself (after fund fees and borrowing costs). Bonds (VGOV) over that period are up 8% total return. In effect a third in 3x, two thirds in bonds beat 100% in 1x over that period due to the 3x having tended to relatively outperform during a prolonged up-trend.

I use 20% rebalance bands, so for example 25% 2x UK stocks initial weighting and rebalance holdings back to target weightings if that drifts to below 0.8 x 25% or rises above 1.2 x 25%. Ditto for 0.8 x 0.167; 1.2 x 0.167 (3x US stock). Since July 2013 there were two rebalance events. One late November 2013, another early September 2014. i.e. you don't need to rebalance that often. Typically once/year is sufficient - but that depends upon volatility etc.

So in a uptrend the 3x rose more than three times the 1x after covering costs, bonds however added to that benefit. If you look how a LETF performs in a prolonged down trend you'll generally see that it declines proportionately less. For example 2008 saw S&P500 total gain down -37% whilst SSO total gain was down -68% and not the -74% that twice the 1x loss would indicate.

In a uptrend as the LETF in effect increases exposure daily, so that scales up rewards. In a down trend as the LETF reduces exposure daily so that slows losses - proportionately. Combined that's beneficial. Countering that - in a zigzag sideways trend/period LETF's relatively lose out. Consider all three, up trend gaining more, down trend losing less, sideways losing out and that tends to broadly all wash.

Since July 2013, 25% 2MCL, 16.7% 3USL, 58.3% VGOV, which is similar to holding 50/50 US stocks/UK stocks, has yielded a 20.8% total gain for a UK investor. Whilst had 50/50 S&P500/FT250 been held a UK investor would be sitting on a 14.9% gain since July 2013. Primarily that benefit arose out of there being a up trend in US stocks. UK stocks in contrast gave up a little as stocks zigzagged (LETF's relatively lost out). Other factors include that bonds did relatively OK (8%, so beat cost of carry/borrowing/leverage), and the GB£ also declined relative to US$ so a UK investor holding some US$ benefited by some FX gains.

If you start looking at how LETF's relatively perform compared to 1x (non leveraged) over periods of more than a single day it tends to become confusing and uncorrelated. The best approach IMO is to look at how half in 2x, half in bonds compares to 100% in 1x over a year long period (i.e. assume that its rebalanced back to 50/50 just once each year) and generally you'll see reasonably close tracking of the two. Look at empirical evidence rather than mathematical model assumptions.
Clive
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Broadly investors are rewarded for taking risks - but not always proportionately so. There are a range of risk factors and often volatility is considered as being one risk factor. Typically rewards can be derived from each of price appreciation, income (dividends, interest), FX (currency fluctuations), volatility capture (rebalance benefits), debt/lending.

Single assets can provide exposure to multiple risks. Stocks for instance typically have debt to equity ratio of 1.0 so they in effect borrow to invest (leveraged) and provide price appreciation (share price) and income (dividend) reward factors. Foreign stocks/earnings add in FX risk/reward. Blend 50/50 or whatever stock/bonds and periodically rebalance and you add in lending (bonds) and volatility capture (rebalance) factors.

Some investors may however focus on just one single risk/reward factor, such as Options Vega (volatility) traders.

My guess is that those factors are all broadly as rewarding as each other, so you might interchange one for another factor to equal overall effect. With leveraging you scale up volatility (rebalance gains potential), at the cost of reducing price appreciation potential.

The ideal choice is perhaps equal measure of exposure to each of the risk/reward factors, as that's more diversified and likely would reduce overall portfolio volatility. Pushing any one single factor alone is likely to induce greater overall portfolio volatility - and when compounded similar average rewards with less volatility is broadly the more rewarding overall choice.
Johno
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Re: Should I use margin to buy a balanced fund?

Post by Johno »

Zb3 wrote:
Johno wrote: Backwardation/contango is not really a meaningful concept for financial futures,
Thanks for the reply. I thought backwardation referred to when the cost of carry was positive - i.e. where the contract trades under the spot price but converges with the spot price at expiry. This is based on the cost to buy and carry until term an equity portfolio based on the underlying index (i.e. SPY for an S&P Emini) - which is a function of dividends and interest rates?

I'm still slightly confused about the implied financing rate. I had a look online but couldn't really find much on it apart from a formula on the CME website. It seemed to me that the implied finance occurrs when the contract is rolled over, although conceptually I don't understand the reason behind the numbers in the formula. I don't understand why there is a financing rate in a futures contract since you are not technically borrowing anything - you are only required to have enough to cover the change in the underlying index, not buy the value of the index itself at expiry.

If the implied financing rate is 0.4% per quarter why would people buy futures contracts at all when they could lend on margin from IB at 1.59%. Also why would people buy a futures contract at invest the rest in the bank at .95% when yearly futures interest costs would be 1.6%? Or is this 0.4% annualised and not a quarterly interest cost?
Johno wrote:Also to get a little more fancy the investor could have some of the 25% in the futures account in say a short term corp bond ETF with a conditional sell order triggered by a drop in the ES big enough to need the extra margin.
This is an interesting idea. Would Interactive Brokers offer this kind of service?
1. Not to get off on a tangent on terminology, you could technically use the term 'backwardation' for the downsloping equity index futures curve (whenever divident yield exceeds financing rate) but IMO it's not very relevant to financial futures where there are no issues of the underlying being unavailable now (wheat yet to be harvested), perishable, or storage facilities being limited, etc. the things that make backwardation/contango meaningful terms for trading decisions in commodities futures.

Anyway, the importance of the financing rate is that it determines the arbitrage free price of the futures contract. If for simplicity we assumed the futures contract had 1/4 year to maturity, and that the market clearing participant could finance stock purchases at a 0.4% *pa*, and the index paid a dividend of 2% pa, and the cash S&P index was trading at 2000, then (with simplified math) the futures price would be 2000*(1+.004/4)/(1+.02/4)~1992. If the contract traded at 1993, you could short it, buy the index basket (financed at .4% pa), collect the 8 points of net carry over the quarter, and have the net capital gain/loss of the index position and contract lose 7 points: 1 free point, and likewise for any other price but 1992, (if below 1992: short the index, earn .4% on that reverse repo, and buying the contract) assuming the financing rate was .4%.

And likewise if one knows the dividend rate, index price and futures price, one can calculate what the financing rate would be. Since after all this rate might vary for every market participant, but still there's some overall rate which represents where the market clears between buyers and sellers of the index and futures contract. As noted, the implied rate has recently been 0.4% *annualized*, therefore substantially lower than 0.95% annualized individuals (but not institutions, in general) can earn on highest paying FDIC insured money market accounts.

2. Yes and as was noted there may be other ways to do the same thing, as in picking order of what gets liquidated first.

As far as brokers allowing futures in IRA's, the other key factor is whether they have low commissions and a good trading platform, since the futures must be rolled (practically speaking) every quarter, with commission and possible bid-offer each time*. IB is far superior to Vanguard or Fidelity for any kind of trading, before you even consider futures. I have accounts which both IB and Vanguard, that doesn't seem to me a real obstacle to the idea.

*So you buy and sell a contract 4 times a year, 8 trades, per ES unit of notional (around $98k right now), $2.04 IB commission, realistic IME to lose only 1/8 tick on bid or offer-mid per trade, 8*($2.04+.125*$50)/$98k~7bps pa in transaction cost, comparable to an ETF, but with the boost of .95%-.4% on a large % of the notional, and/or ability to take credit/duration risk of bond ETF and equity risk of futures at the same time, and get the expected return, though also the risk, of both.
Park
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Re: Should I use margin to buy a balanced fund?

Post by Park »

About rebalancing leveraged ETFs, I’d like to make a cautionary note. The links above discuss rebalancing with 2X ETFs: I can’t find a paper looking at 3X ETFs and rebalancing.

What distinguishes leveraged ETFs from other types of leverage is the constant leverage. The leverage ratio is the ratio of total assets (debt and equity) to equity. With a margin loan, debt stays constant, but equity varies; therefore, the leverage ratio varies. With leveraged ETFs, that leverage ratio of total assets to equity stays constant.

Assume your portfolio is 100 shares of company A, and each share cost $1. Half of the shares were bought using borrowed money. Assume the value of company A shares go up 25% in the first day, and down 20% the next day. With a constant debt strategy, you’re back to where you started.

Let’s use the same scenario, but with a constant leverage strategy. On the first day, the portfolio increases in value to $125. Prior to rebalancing, your equity is $75 and your debt is $50. But with a constant leverage ratio, you want debt and equity to be the same. So you buy $25 of company A stock. Company A stock now costs $1.25, so you buy 20 shares at that price. After rebalancing at the end of the first day, you have $75 in equity and $75 in debt, with total assets of $150. On the second day, the value of company A stock goes down 20% to $1. Your total assets have decreased to $120. Prior to rebalancing on the second day, you have $45 in equity and $75 in debt. To get back to a leverage ratio of 2, you sell $30 of company A shares at $1 each. You now have 90 shares, which are worth $1 each. You have lost $10, unlike the constant debt strategy, where there was no gain or loss.

To maintain a constant leverage ratio, one rebalances, and that results in buying high and selling low. With a constant leverage strategy, you’re not exposed to margin calls, but the price you pay for that is the rebalancing cost.

The higher the volatility, the higher the rebalancing cost. When volatility is very low, the cost is minimal. But if volatility gets high enough, it will make a constant leverage strategy counterproductive.

http://www.iijournals.com/doi/abs/10.39 ... 11.1.4.066

I’m going to go into the above link in more detail. The following numbers use the CRSP value weighted index from January 1926 to December 2009. They ignore costs and taxes. The annualized rate of return of the index was 9.66%. If the index was levered 2X and the leverage was rebalanced daily, the annualized return was 16.71%. For 3X leverage, the return was 20.46%.

Before you decide to convert your portfolio to 3X leveraged ETFs, read this paragraph. The author doesn’t state whether the following results are with 2X or 3X leverage. He mentions a 99.8% loss during the 1929 market crash. From October 2007 to December 2008, there is a 93% loss. Entry and exit points matter.

He takes the same data base, and divides the return of each year into low volatility and high volatility categories. The dividing line is whether the monthly volatility (annualized) of the last year was more or less than 18.6%. He gives “average arithmetic annual returns based on rolling yearly periods”. For high volatility periods from 1926 to 2009, index, 2X and 3X returns were -1.4%, -2.3% and -3.7% respectively. For low volatility periods, the returns were 15.2%, 33.5% and 55.5%.

Volatility matters. However, returns also matter. The following uses the same assumptions as the last paragraph, but looks at data from 1990 to 1999. Even in the high volatility periods during this time, the respective returns were 12.2%, 21.7% and 27.3%. So higher returns can overcome high volatility.

The author also did a Monte Carlo simulation. The following assumes average annual returns of 6-12%, leverage rebalanced daily and ignores costs and taxes. With a 15% standard deviation, index, 2X and 3X returns are 9%, 16.2% and 21.2%. With a 20% standard deviation, the numbers are 9%, 14.2% and 15%. As standard deviation increases, leverage return decreases, and higher leverage ratios are effected more.

Assume the same scenario as the last paragraph, but average annual returns are 0-6% and standard deviation is 20%. Index, 2X and 3X returns are 3%, 2% and -2.9%. Volatility has overwhelmed the leverage effect.

Assume the same scenario as in the last two paragraphs, but average annual returns are 12-18% and standard deviation is 20%. Index, 2X and 3X returns are 15%, 27.1% and 35%. The increased return outweighs the volatility drag.

The author outlines a strategy where the VIX is used to predict volatility. The VIX average from January 1990 to December 2009 was 20.2%. He mentions that the annualized daily volatility is a bit less than that, and that this overestimate decreased from 5% to 2% in 2003. In this strategy, the investor switches from index funds to constant leveraged funds when the VIX is less than 20, and vice versa when it is greater than 20. He compares this switching strategy to a buy and hold strategy of constant leveraged funds. He shows that from 1990 to 2009, results are similar, but the Sharpe ratio is higher for the switching strategy. From 1990 to 1999, the buy and hold strategy outperforms. But from 2000 to 2009, the buy and hold strategy results in losses, whereas the switching strategy results in gains. As mentioned previously, the high returns of 1990-1999 probably overcame the volatility drag.

In a previous post, several links were given to papers describing a rebalancing strategy when using leveraged ETFs. Leveraged ETFs sell when prices decline and buy when prices increase. The rebalancing strategy buys when prices decline and sell when prices increase. This counteracts the rebalancing losses inherent in a constant leverage strategy. One possible downside to this strategy is that money has to be set aside to buy shares when prices decline.

The link in this post describes a different strategy. When volatility is low, use leveraged ETFs. When volatility is high, use unleveraged index funds.

A case could be made for combining both strategies. Assume returns are in the 6-12% range. The following comes from the Monte Carlo simulation. With a standard deviation of 10%, returns of the index, 2X constant leveraged strategy and 3X constant leveraged strategy are 9%, 17.7% and 25.8% respectively. So rebalancing might make sense for a 3X fund at this SD, although a case could be made for buy and hold. With a standard deviation of 15%, returns are 9%, 16.2% and 21.2%. A better case could be made for rebalancing, especially the 3X fund. With a standard deviation of 20%, returns are 9%, 14.2% and 15%. One should rebalance or possibly switch to unleveraged funds. With a standard deviation of 25%, returns are 9%, 11.6% and 7.4%. The case for switching to unleveraged funds, as opposed to rebalancing, becomes better. Remember that these returns don’t take into account costs

Comments, including criticisms, are most welcome. I have edited the part prior to the link being given, to make the rebalancing cost aspect of constant leverage clearer.
Last edited by Park on Tue Oct 28, 2014 3:10 pm, edited 1 time in total.
Beliavsky
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Re: Should I use margin to buy a balanced fund?

Post by Beliavsky »

Thanks to Park for his detailed discussion of the paper "Solving the Leveraged ETF Compounding Problem" by William J. Trainor. This paper is not freely available, but another paper he co-authored, "Forecasting Holding Periods for Leveraged ETFs Using Decay Thresholds: Theory and Applications" is available.
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Kevin M
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Rob Bertram wrote: Compound annual growth rate (CAGR) / geometric mean is a very important measure that we only know after the fact. MPT uses arithmetic mean and standard deviation, but the article you posted gives an approximation for calculating expected CAGR from arithmetic mean and standard deviation.
We also only know arithmetic mean and standard deviation of future returns after the fact, so in this respect there is no difference between them and geometric mean. You can calculate any of them for historical results. There's no need to estimate geometric mean from the other two--just calculate it from your data series.

MPT uses arithmetic mean because that is the statistical expected value of a probability distribution of estimated future returns over a single holding period.

When you say "MPT uses arithmetic mean ...", I think what you might mean is that some people calculate arithmetic means and standard deviations from historical results, then either create pretty but meaningless efficient frontiers based on the past, or use historical results as a proxy for expected returns going forward (which is kind of the same thing). Neither one of these is MPT as defined by Markowitz and extended (e.g., CAPM) by Sharpe and others.

Since expected returns and expected standard deviations can't be observed, academics and practitioners have focused their analyses on historical results. Academics ask questions like, "if CAPM is an accurate model, why didn't the historical results from a certain period fit the model?" Markowitz himself did not use CAPM to decide on his own portfolio construction (or so I've read).

As I've said before, MPT/CAPM deal with single, future holding period returns, so the calculation of a geometric mean is meaningless, and an efficient frontier based on past results is irrelevant. If you want to twist MPT/CAPM to your own purposes, there's no reason you can't use geometric mean instead of arithmetic mean on the vertical axis.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
Johno
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Re: Should I use margin to buy a balanced fund?

Post by Johno »

Park wrote:About rebalancing leveraged ETFs, I’d like to make a cautionary note. The links above discuss rebalancing with 2X ETFs: I can’t find a paper looking at 3X ETFs and rebalancing.

In a previous post, several links were given to papers describing a rebalancing strategy when using leveraged ETFs. Leveraged ETFs sell when prices decline and buy when prices increase. The rebalancing strategy buys when prices decline and sell when prices increase. This counteracts the rebalancing losses inherent in a constant leverage strategy. One possible downside to this strategy is that money has to be set aside to buy shares when prices decline.

The link in this post describes a different strategy. When volatility is low, use leveraged ETFs. When volatility is high, use unleveraged index funds.

Remember that these returns don’t take into account costs
I take it as given when using leveraged ETF's that you'd rebalance the number of ETF shares to match the notional position you want. I cases where I've used such funds it's generally as a spread trade against the S&P futures, eg. if my whole portfolio is at least temporarily too long emerging markets, it's more tax efficient to buy ES futures and buy 3X inverse leveraged emerging markets ETF, in IRA, than to actually sell conventional emerging markets index funds I have in taxable accounts and pay capital gains. After all the imbalance might reverse with market moves, then I'd be buying back the same conventional fund shares after paying cg's on the old ones. Anyway if I do such a trade I automatically want the EM 3X inverse ETF position to match and integer number of futures contracts, so will sell high and buy low to keep it that way. Of course that has (bid offer mainly) transactions cost. And also the typical 3X ETF has expense ratio around .95%, so ~.32% per leg, non negligibly greater than a conventional fund of lowest cost. I believe it can make sense for interim rebalancing to avoid taxes, but as a long term investment on its own that's another thing.

The interesting discussion you gave of the research seems about as expected, mainly confirms the conventional wisdom that the difference between 3X daily and the long term performance can be a killer when the market is especially volatile and the investor just lets the ETF ride, in contradiction to its stated purpose as daily/short term hedge (or speculation) vehicle. Maybe it's needless to say, but the constant leverage feature is not there just of the benefit of avoiding margin calls, but that the product wouldn't be marketable if it was 'the used to be 3X leveraged, but now it's 2.8365X leveraged due to what happened yesterday' fund. :D

On the topic of 'volatility adapted' if you will rebalancing, I'd reiterate the idea of put writing in lieu of being outright long the market. Per CBOE data for 1988-2011 selling a one month at-money-put on the S&P every month for a given notional (say sell one put on the ES contract rather than being long one ES contract) not only had a significantly higher Sharpe ratio than being long the underlying but, rather remarkably, beat the underlying in absolute return as well in the period. Put prices naturally adjust upward when the market is unsettled (VIX high), arguably too much. Those findings also don't include that fact that the put trade also allows the individual investor to put most of the money* in FDIC insured account at significantly higher rate than the funding rate implied by the option price.
http://www.cboe.com/micro/buywrite/Pap- ... eb2012.pdf

*assuming puts written on the futures, margin requirement for puts written on physical stocks (including broad ETF's) is much higher; same caveats and limitations to be able to withstand large one day moves as with being long the futures.
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