Should I use margin to buy a balanced fund?

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

Post by Kevin M »

The mortgage thing was more of an aside. The important point is that a margin loan rate is not the correct rate to use as the risk-free rate in CAPM for a longer-term holding period. Current mortgage rates are closer, but of course not perfect either.

Once again, by definition the riskless rate in the CAPM model has zero uncertainty for the specified holding period; i.e., the standard deviation of expected return is 0%. This clearly is not the case for a variable rate loan. Rob has asked for the flaws in his thinking, and this is a big one.

Rob, I owe you a reply to your initial objections to my reply in which I first presented one of my CAPM charts. I don't have time for that now, but I plan on providing it later. I realize that until I've done so, you're unlikely to accept my explanation of the flaws in the way you're thinking about it (your model). Stay tuned ...

I can't resist one more comment on the mortgage thing. "who puts 50% plus of their CAPM leveraged portfolio in undiversified real estate?" Everyone who has a mortgage and financial assets, if they look at their "portfolio" holistically, and applies the CAPM model to it. This has been discussed extensively in other threads, so I'll leave it at that for now. I'm happy to agree to disagree on this in the context of this thread.

Kevin
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lee1026
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

I agree with the point about mortgages and the call option. And I want to add that in many states where the mortgage is non-recourse, the mortgage also comes with a free put option of defaulting on the mortgage and mailing back the keys. Also worth quite a bit. On the downside, if you sell the house, you have no choice other to pay off mortgage, no matter how low the rate on that mortgage is, so there is that.

Back to the discussions of the 10 year time horizons and estimates on returns. I disagree heavily with the estimate on returns, but I want to put that aside for a more important argument: Very few people invests at a long term time horizon. Evidence that very few people invests like that can be seen in the marketplace for investments. For someone with a long term time horizon, the risk-less asset is the treasury STRIPS of the correct duration. Everything else is more risky. A normal 30 year have reinvestment risk on the coupons relative to the STRIPS. But most bonds are sold as normal bonds instead of STRIPS, and the yield curve is curved in such a way that the 30 year STRIPS have considerable risk premium attached. In theory, TIPS STRIPS would be one of the most popular investment options, and yet it isn't even being sold.

Instead, when a person is young, retirement savings might be labelled as retirement saving, but it is also the defacto downpayment fund, college tuition fund, disability insurance, and as a hedge to career risk. By the time that he is old enough to not have to worry about all that, retirement isn't so far away anymore, but one's retirement drawdown schedule is always quite uncertain. Maybe I just have an attention-span of a gold fish, but I consider my investment horizon to be around a month. And given how Rob says he will rebalance, it seems like that he effectively does the same.

And over 30 years, it is hard to say what risk what even means. For a dramatic example of this, consider what would have happened to a hypothetical person who thought that inflation adjusted Chinese government bonds in the 1984 was a risk-less asset. No such assets existed at the time, but we can easily imagine the properties - it would pay around 2-3% (going interest at the time), and keep up with inflation. Well, fast forward to 2014, this person would find himself a pauper. In 1984, a normal family in urban China spent around 50-80% of its income on food. In 2014, it is down to 20-30%. His bonds kept up in terms of what he can buy, but what you have to buy to be considered a respectable member of society changed drastically. The change is so dramatically that the grades of goods that he have expected to buy often isn't even sold anymore. His money kept up with inflation in the the sense that it will buy him the same shabby life in 1984, but in 2014, that is a pauper's life. We probably shouldn't expected the United States to undergo that kind of change in the next 30 years, but I am counting on nothing to stay the same over that kind of time.
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Kevin M wrote:Once again, by definition the riskless rate in the CAPM model has zero uncertainty for the specified holding period; i.e., the standard deviation of expected return is 0%. This clearly is not the case for a variable rate loan. Rob has asked for the flaws in his thinking, and this is a big one.
Part of me tries to keep things as simple as possible. I'm not trying to predict future returns. Instead, I'm trying to justify leveraging a balanced portfolio over an indefinite "long term." Maybe CAPM might be overkill for that in the sense that I'm using a cannon to kill a fly. CAPM allows for pricing of much more specific assets. It's a lot of utility that I don't need in this context.

James Tobin's Separation Theorem might be enough. It lets us draw the CML/CAL as a straight line through the super-efficient portfolio. That's all that I need. It doesn't change the fact that this also assumes that there's no variability in the risk-free rate.

In reality, as you and ogd point out, there could be times when the risk-free (margin) rate increases, but the market takes time to adjust. During that period, the CAL would drop below the efficient frontier. Backtesting shows that the 2.5x leverage strategy (with +1.5% margin rate) beats the total stock market roughly 70% of the time. So there definitely are times (years) when a non-leveraged strategy would have done better. However, over the long run, leveraging appears to have higher returns with equal risk.
Kevin M wrote:Rob, I owe you a reply to your initial objections to my reply in which I first presented one of my CAPM charts. I don't have time for that now, but I plan on providing it later. I realize that until I've done so, you're unlikely to accept my explanation of the flaws in the way you're thinking about it (your model). Stay tuned ...
There's no rush. I don't even remember what that objection was. My main concern is that we can't predict the future. We can model the past and explain what happened, but that does not allow us to predict far into the future. We can try to model the future based on some (pessimistic) educated assumptions on the future market, but it's no better or worse than backtesting.
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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, let me try to address this topic you keep bringing up about trying to predict the future vs. backtesting.

If you are going to use CAPM as a justification for your experiment, you must base it on estimates of expected values for future returns, variances, and covariances; if you don't understand this, please read some more about CAPM. You can choose to simply use historical values as the basis for your expected values (which I think is a mistake, especially for bonds), but you should at least understand that this is what your'e doing.

Perhaps you are getting confused because academics use historical data to evaluate how well CAPM predicted returns in the past. Academics and practitioners also may use historical returns, variances and covariances as components in developing their estimates of expected future values for these parameters, but typically adjustments are made to reflect current economic conditions.

Whether you realize it or not, you are making predictions about the future just as much as anything I've presented. Inherent in your approach is the assumption that the future will resemble the past, which is a prediction about the future. The charts you've presented imply a belief that future returns will be similar to past returns (ditto for standard deviations and correlations); i.e., you are using historical values as your expected values. The primary thing I'm doing differently is adjusting the expected values to better reflect current economic conditions. This is easiest to do for bonds; for stocks it's much harder to develop reliable expected values.

I believe there's pretty wide agreement that the current yield is a reasonable estimate for the expected return for the US total bond market over the next 5-10 years. As I mentioned, Vanguard has a research paper that shows very high correlation between YTM and subsequent 10-year returns. I can't find that paper now, but I did find a VG research paper published January 2014 that states this:
the expected ten-year median return of the broad taxable U.S. fixed income market is centered in the 1.5%–3.0% range
So we should at least be able to agree that it's extremely unlikely you're going to see bond returns in the 7%-8% range (as shown on your charts) over the next 5-10 years. If you understand how bond price, yield and duration work, you should be able to work that out for yourself by evaluating various interest-rate scenarios.

As I said, developing estimates for expected returns for stocks is more complicated, but here is a long, but very interesting, paper on different ways of developing estimates of the equity risk premium: Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2013 Edition by Aswath Damodaran :: SSRN.

Not directly related to the "predicting the future topic", but also very important: I've already pointed out what I think is a huge error on your part by showing a risk-free lending rate of 0% on your historical charts when the risk-free lending rate for that period (T-bills) averaged close to 5%; this would result in an average risk-free borrowing rate of about 6%-6.5% if you assume borrowing at 1%-1.5% over the T-bill rate. Please at least correct this or explain why you think it makes sense to assume today's borrowing rate in yesterday's world.

If your rationale is just that leveraging Wellesley worked well in the past, so you're hoping that it will work similarly well in the future, then I have nothing else to say except "good luck". But if you want to bring CAPM into the discussion (which is the part I'm mainly interested in), then it probably is worthwhile to do some more homework to try and understand the model better, how it might make sense to use it in portfolio construction, its limitations, and the mistakes you are making in trying to apply it and use it to justify what you're doing.

I'm interested in learning more about it as well. For example, I've never run across any good explanations about how it can be applied to portfolio construction for longer-term holding periods, which it seems is what you're trying to do.

Kevin
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lee1026
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

So we should at least be able to agree that it's extremely unlikely you're going to see bond returns in the 7%-8% range (as shown on your charts) over the next 5-10 years. If you understand how bond price, yield and duration work, you should be able to work that out for yourself by evaluating various interest-rate scenarios.
He backtested with FFR+1.5% for the past. Considering that FFR was around 5-6% in the period that he backtested, the difference between bond yields and what he would be paying is more or less normal. The big problem with his backtest is actually the sheer alpha that the fund had in the past. I am somewhat optimistic that it will continue, but that is a whole other discussion entirely.

I still think that you are beating a strawman with you model. Most of his borrowing, especially in 10 years, is going to be 1% above the FFR. The difference between 1% + FFR is going to be at $50 a month over what he actually pays, at most. That is "worry more about commissions and bid ask spread" land. And the vanguard paper you linked to is about CAGRs over the next 10 years. For the CAPM, we use arithmetic averages! And since you are using that vanguard paper, it also provides its estimates to the return of balanced portfolios. (Look on page 27)

It didn't provide an estimate to 60% bonds, 40% stocks, but it did for 40% bonds, 60% stock: Real returns range from 1.3%-7.1%, with volatility of 11.2%.

For 20% bonds, 80% stock, it is 1.7% to 9%, with volatility of 14.4%.

If he going to be borrowing at a real rate of more or less zero (assuming an average FFR of 1% in the next 10 years, and inflation 2%), then leveraging the returns of the 40/60 1.3x will return somewhere between 1.7% to 9.23%, beating the 20/80, and probably the 100% stocks. (I didn't find inflation estimates in the paper, and only stock returns in nominal terms.)
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Kevin M
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

The following chart shows the CAPM results basing expected parameter values on the 1972-2013 data for total US stocks and total US bonds (using data from PortfolioVisualizer site). The T-Bill/Money market values are used as a proxy for the riskless lending rate, and I added 1.2% to this for the riskless borrowing rate (Rob stated in a previous reply that he expected this to be his average incremental rate over the federal funds rate). Separate Capital Allocation Lines (CALs) are constructed for lending (green) and borrowing (red), with a 40/60 stock/bond portfolio as the risky portfolio.

Image

Hopefully it's obvious that the expected returns are much higher than in the current economy, but I wanted to share a more realistic view based on historical data than the charts Rob has shared, the main difference being the use of more realistic riskless rates for the historical data.

One caveat is that the proxy for the riskless rates aren't actually riskless. The standard deviation for T-bill/money market for this period was 3.33%, not 0%. Nevertheless, if we consider this chart as representing expectations for a one-year holding period in an economy for which these historical values would be realistic, this is an OK approximation, since a 1-year T-bill provides a certain 1-year nominal return. Perhaps it's a bit more of a stretch for the borrowing rate, since I don't believe you can lock in a 1-year rate for a margin loan (but please correct me if I'm wrong), but still probably not too bad an approximation.

The way to think about this is in CAPM terms is that each year in the data series represents a scenario with probability 1/N (N = number of years in the data series = 42). The resulting average expected returns and standard deviations are estimates for a one-year holding period in an economy for which the historical results would represent realistic expectations.

Note that the correlation between stocks and bonds over this time period was a slightly positive value of +0.21.

This analysis still shows a somewhat beneficial effect of leveraging a 40/60 portfolio. As highlighted in the table below the chart, the same expected return (ER=12%) as a 100% stock portfolio is achieved with a reduction in standard deviation (SD) of about 2% (16.4 vs. 18.3), or a slightly higher ER (12.7% vs. 12%) is achieved with the same SD of 18.3%.

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

Post by lee1026 »

One caveat is that the proxy for the riskless rates aren't actually riskless. The standard deviation for T-bill/money market for this period was 3.33%, not 0%. Nevertheless, if we consider this chart as representing expectations for a one-year holding period in an economy for which these historical values would be realistic, this is an OK approximation, since a 1-year T-bill provides a certain 1-year nominal return. Perhaps it's a bit more of a stretch for the borrowing rate, since I don't believe you can lock in a 1-year rate for a margin loan (but please correct me if I'm wrong), but still probably not too bad an approximation.
You can hedge the 1 year rate on the margin rate via the futures market for the federal funds rate. You will be paying IB more if the rates change, but then you will be getting money via the futures market, so it is a wash if you do it right. If it goes the other way, you will be paying on the futures market, but paying IB less. Of course, then you would be borrowing at the 1% + 1 year rate when all is said and done, but you can do it if you really want to. You can lock down the rate for up to 10 years using the Eurodollar futures market.
I added 1.2% to this for the riskless borrowing rate
Those numbers are based on the 3 month rate, The federal funds rate is generally smaller by around 15-20 points.
The standard deviation for T-bill/money market for this period was 3.33%, not 0%.
Because you are looking at things over 42 years. T-Bills have never deviated from what people expected them to return on a short term basis. Or to put it differently, it is really hard to lose a lot of money in T-bills. T-Bills returns over the 30 years are very uncertain, but a 30 year STIRPS returns are completely known in advance.
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Re: Should I use margin to buy a balanced fund?

Post by ogd »

Kevin M wrote:ogd, the charts I'm showing are purely based on simple math and estimates of expected returns, standard deviations, and correlation; nothing at all to do with backtests. Two standard MPT equations are used to construct the efficient frontier for two risky assets, and one simple equation is used to construct the CAL (weighted expected return using ERs for the riskless asset and the selected risky portfolio). The degree to which the model predicts the future is entirely dependent on how close the estimates end up being to actual results, and to how well reality reflects the assumptions built into the model.
Kevin: thanks for giving me the incentive to finally understand all the CAPM stuff, including the tricky bent-tangent graphs. I get it now. And I too think that it's more reasonable to project return estimates than to use backtests. Although, I'd point one thing out: one thing that's still left strongly dependent on backtests is correlation. I was pointing out earlier (and I remember you saying the same in a thread many moons ago) that from low interest rates you can't expect bonds to have nearly as much correlation with stocks, at least in the good sense -- increasing in value during a crash.

Anyway, good discussion.
Kevin M wrote:I can't resist one more comment on the mortgage thing. "who puts 50% plus of their CAPM leveraged portfolio in undiversified real estate?" Everyone who has a mortgage and financial assets, if they look at their "portfolio" holistically, and applies the CAPM model to it. This has been discussed extensively in other threads, so I'll leave it at that for now. I'm happy to agree to disagree on this in the context of this thread.
What I meant is this: who does this because they think of it as improving efficiency under CAPM? Nobody. It's obvious that the decision to acquire the mortgage/house combo is driven by external factors, kids, dogs, view etc. You can't just say that if that is okay then this is okay, when that involves so many other things. And you can't exclude the house from the discussion either because that gigantic pile of real estate makes the portfolio look entirely different and you not nearly as leveraged. Anyway, I agree, long story, while disagreeing that every home owner is doing this in disguise.
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Kevin, thank you for providing the models and the graphs. It is much appreciated and very useful. I agree that a shortfall of my application of CAPM is that I plan to use this strategy long term when CAPM is only capable of modeling short-term behavior. My biggest mental struggle with estimating future returns is that we do a respectable job approximating the next 5-10 years, but we're only guessing at what will happen in 30 or 40. Historic returns might give us a better longer-term picture of the shape of the efficient frontier. However, I agree that we need to adjust the returns for a reasonable expectation of interest rates.

I don't know if there's a good design for a "forever" model. I liked what Berntson was doing by looking at historic returns minus the risk-free rate. And that is essentially what you are doing by picking a risk-free rate equal to the historic in one of your graphs. The shape of the curve remains the same, but the curve moves in absolute position.

I understand why CAPM uses arithmetic average as it is attempting to explain what will happen in the next period -- as the future period will probably look like one of the previous periods. This doesn't work so well for the "forever" model where future periods compound. Returns will need to look more like a CAGR than arithmetic average. And, of course, this is a problem with me trying to use CAPM in a way that it was not designed. Ideally, I would like to use CAGR as the efficient frontier. I don't know if I can still draw the leveraged CAL or if it becomes a curve.
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Re: Should I use margin to buy a balanced fund?

Post by Spec7re »

Kevin,

I'd be interested is seeing the same graph done with a 20/80 portfolio of risky stock and treasury futures.

Stock would be a combination of SV, ISV, and EM with a ER of 6.5 and an SD of 22.

Treasury futures would be an ER of 2.5 and an SD of 8.

The correlation for these two should be in the -0.3 range.

The borrowing rate for the treasury futures is the FFR, so the effective borrowing rate for the whole portfolio would be 0.8*FFR.

I feel like this would paint a much more attractive picture of the leveraged portfolio.
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Re: Should I use margin to buy a balanced fund?

Post by jaab »

Maybe of interest here? In a DFA PDF they compare levered Risk Parity portfolios with regular 60/40 portfolios around the world. 1930-2010, using the local T-Bill rate. While RP is not a fixed AA but changes somewhat, it usually ends around 30/70 or so, on average. http://www.texpers.org/documents/confer ... 201202.pdf (page 26).
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Spec7re wrote:I'd be interested is seeing the same graph done with a 20/80 portfolio of risky stock and treasury futures.

Stock would be a combination of SV, ISV, and EM with a ER of 6.5 and an SD of 22.
I think that the equation gets a lot more complicated with 4 funds and rebalancing. But it would be a good homework exercise to describe the model.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

jaab wrote:Maybe of interest here? In a DFA PDF they compare levered Risk Parity portfolios with regular 60/40 portfolios around the world. 1930-2010, using the local T-Bill rate. While RP is not a fixed AA but changes somewhat, it usually ends around 30/70 or so, on average. http://www.texpers.org/documents/confer ... 201202.pdf (page 26).
Thanks for that link! I don't understand the mechanics of their Risk Parity portfolio, but it seems to be in line with what I'm trying to do.
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Re: Should I use margin to buy a balanced fund?

Post by jaab »

After digging through the PDF I think they are using bills, Gov LT bonds and equities. This is because they mention the DMS data set and bonds there are Gov LT, AFAIK. They create RP portfolios (equal volatility contribution) based on the prior 30 year data and rebalance once a year. Then lever up in hindsight to match the risk of 60/40. DMS data starts in 1900, this explains 1930 as first year of the actual backtest.

In their test it's not bad, but not really better either. Basically you just exchange equity risk and duration risk. And this means the relative result to 60/40 depends mostly on (future) inflation/interest rate behaviour (see page 27). Don't know what happens when you add corporate bonds and use medium duration (i.e. TBM or a W-fund) and a fixed AA though.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Spec7re: glad to oblige, but I don't understand this:
The borrowing rate for the treasury futures is the FFR, so the effective borrowing rate for the whole portfolio would be 0.8*FFR.
If I read it literally it says borrowing rate would be 0.8 x 0.09% = 0.072%. You can borrow at less than the federal funds rate? Or are you saying you can borrow at FFR (0.09%) on up to 80% of the value of the portfolio?

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

Post by Kevin M »

Rob Bertram wrote:
Spec7re wrote:I'd be interested is seeing the same graph done with a 20/80 portfolio of risky stock and treasury futures.

Stock would be a combination of SV, ISV, and EM with a ER of 6.5 and an SD of 22.
I think that the equation gets a lot more complicated with 4 funds and rebalancing. But it would be a good homework exercise to describe the model.
The stocks would still be modeled as one of the two risky portfolios used to construct the EF, using the ER and SD provided. The model would be based on holding the predetermined proportion of these stocks that resulted in these ER/SD estimates at the beginning of the (one year) holding period. I don't need to know anything about what's in the stock black box--just the resulting ER, SD and CORREL with the bond component. The assumption would be that at the end of the one-year holding period everything would be rebalanced back to original weights for the next one-year holding period. Of course changing economic conditions, updated ER estimates, etc., could warrant some portfolio changes and model parameter updates for the next holding period (dealer's choice).

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

Post by Spec7re »

The second statement. 0.8 because you are only borrowing 80% of the portfolio. 0.8*3 mo T-bill might be a better/more conservative estimation. Lee would probably know what the best estimation of the implied financing rate on treasury futures is.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Spec7re wrote:Kevin,

I'd be interested is seeing the same graph done with a 20/80 portfolio of risky stock and treasury futures. Stock would be a combination of SV, ISV, and EM with a ER of 6.5 and an SD of 22. Treasury futures would be an ER of 2.5 and an SD of 8. The correlation for these two should be in the -0.3 range. The borrowing rate for the treasury futures is the FFR, so the effective borrowing rate for the whole portfolio would be 0.8*FFR.
Assuming I'm understanding you correctly, below is the CAPM model for this. Rounded FFR to 0.1, which you're saying is your borrowing rate, and used same for lending rate (not applicable here anyway).

[Image

Assuming you can only borrow 100% of value of T-futures, then the highlighted row in the table below the chart is the best you can do (1.8X leverage), which is about ER = 6% with SD = 12%. If you could somehow borrow more at this rate, you could achieve 100% stock ER = 6.5% and SD about 13% with 2X leverage. And with 3.3X leverage you get ER of about 11% with SD close to 100% stock SD of about 22.

As a side note, the 30/70 portfolio has slightly higher Sharpe, but not significantly different than 20/80, as is apparent from eyeballing the chart.

As always, this is just a model, and validity is hugely dependent on how close estimated parameters end up being to realized parameters.

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

Post by Spec7re »

Kevin M wrote:
Spec7re wrote:Kevin,

I'd be interested is seeing the same graph done with a 20/80 portfolio of risky stock and treasury futures. Stock would be a combination of SV, ISV, and EM with a ER of 6.5 and an SD of 22. Treasury futures would be an ER of 2.5 and an SD of 8. The correlation for these two should be in the -0.3 range. The borrowing rate for the treasury futures is the FFR, so the effective borrowing rate for the whole portfolio would be 0.8*FFR.
Assuming I'm understanding you correctly, below is the CAPM model for this. Rounded FFR to 0.1, which you're saying is your borrowing rate, and used same for lending rate (not applicable here anyway).

[Image

Assuming you can only borrow 100% of value of T-futures, then the highlighted row in the table below the chart is the best you can do (1.8X leverage), which is about ER = 6% with SD = 12%. If you could somehow borrow more at this rate, you could achieve 100% stock ER = 6.5% and SD about 13% with 2X leverage. And with 3.3X leverage you get ER of about 11% with SD close to 100% stock SD of about 22.

As a side note, the 30/70 portfolio has slightly higher Sharpe, but not significantly different than 20/80, as is apparent from eyeballing the chart.

As always, this is just a model, and validity is hugely dependent on how close estimated parameters end up being to realized parameters.

Kevin
Awesome, thanks for doing this.

I'm not sure how you get a max of 1.8x leverage. You can get a 100,000 face value T-note future with less than $2000 in your account (over 50x), although you would probably want to hold more cash in the margin account so you are not constantly facing a margin call. Max leverage should be just less than 100%/20%=5x. 4x is probably a reasonable number to use as max for the 20/80 portfolio.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Spec7re wrote: I'm not sure how you get a max of 1.8x leverage.
I was confused by your 0.8 factor. If it's not a limiting factor on how much you can borrow, then I don't understand its relevance. Why didn't you just say that you can borrow at the FFR? I don't understand how the ratio of futures to stocks has anything to do with the rate, but I don't know much about margin and futures (and didn't really follow those discussions in this thread, since it's not what OP is doing).

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

Post by Spec7re »

I may be misunderstanding something. The borrowing rate only applies to the 80% of the portfolio made up of futures. So I'm assuming if the borrowing rate for futures is X, then the borrowing rate for the portfolio as a whole is 0.8*X, which would be the y intercept of the leveraged line on the graph. I'm still learning all this stuff, so I could easily be wrong.
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

No, the y-intercept of the leveraged line is your entire borrowing/lending rate. For you, that will be the FFR.
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Re: Should I use margin to buy a balanced fund?

Post by Spec7re »

That makes sense now that I think about it. I think I was confused by some posts earlier in the thread. Ignore the 0.8.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

I promised everyone updates. I want to show the experimental portfolio's performance, but I'm looking for an easy way to do it. Posting screen shots of a spreadsheet might be convenient, but it doesn't allow for easy quoting for discussion which I feel is important. At least, I'm still hoping for honest and frank discussions.

Anyway, I can at least list some observations as I go through the experiment:
  • When starting up, there is a lot of waiting. It is probably less of an issue once implemented as one can lever up slightly in anticipation of the transaction.
    1. Specifically with Interactive Brokers, there is a 4-day wait on ACH bank transfers. The same applies to one-time and periodic transfers. Since I plan on doing things on the first trading day of the month, I would need to schedule an automatic payment to start on the 24th of the prior month for it to clear in time.
    2. Mutual funds take 30 days before they can be used in a Reg T margin account.
    3. Mutual fund purchases take a day to execute.
  • Mutual funds cannot be bought on margin. (I didn't know this before I started.) I can borrow against the equity in my mutual fund position (after 30 days), but I cannot borrow to buy a mutual fund. I can, however, buy VTI (ETF for Vanguard's Total Stock Market) and BND (ETF for Vanguard's Total Bond Market) on margin. So half of my portfolio is Wellesley, the other half is 40/60 VTI/BND.
  • Reg T margin accounts only allow borrowing up to 2x leverage for long ETF positions (50% initial margin). Well, the SMA calculation is more complicated than that, but it's close enough. It's enough leverage for my experiment, but I would eventually like to go past that limit assuming everything behaves the way I think. There are two ways to get more leverage. The first would be to use futures. The second is to upgrade to a Portfolio Margin account. With a PM account, mutual funds aren't allowed, so I would need to go with my 2-fund portfolio. Actually, I could go to the 3-fund portfolio which would be within the realm of ideal. (I like global stocks, but I'm not convinced that global bonds are worth the effort.)
I need to spend more time understanding options and futures. I know that there are S&P 500 index futures which are sufficiently diverse, but I don't know of a similar bond future. The nice thing is that I believe margin rates are built into the futures price, and it's fairly low right now, less than what IB charges. The bad thing is that contract sizes are still fairly large (even for e-minis) relative to the size of my portfolio, so I would still need to pick up some VTI and BND positions to fill in the gaps. (I prefer to avoid complexity if possible. But if I'm juggling 3 positions now, I can manage 4-5 without much more difficulty.)

The nice thing about a portfolio margin account is that the maintenance margin is significantly lower than the 25% of a Reg T account. At least, it's lower for diversified funds like VTI (8%) and BND (15%) or about 12.2% for a 40/60 portfolio if my math is correct. (There's an online calculator if you want to try a different portfolio). Initial margin is also the maintenance margin (max 8x leverage in this case) which means I can go past 2x leverage out of the gate. It also means that the call risk drops significantly to the point of improbable (but always possible). For 2.5x and 3x leverage and 12.2% maint margin, the portfolio would need to drop 31.66% and 24.07%, respectively, in order to trigger a margin call.

IB only allows investors with at least $110,000 to open a portfolio margin account or to upgrade from a Reg T margin account. Since I'm starting with 50k and adding 3k monthly, I have 20 months or so before I hit 110k. That should be enough time to see if the leverage experiment behaves the way I expect. Also, mutual funds aren't allowed in a portfolio margin account, so I would need to sell Wellington and only have my 2(or 3)-fund portfolio.
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Re: Should I use margin to buy a balanced fund?

Post by Tanelorn »

You can hold mutual funds in a PM account, but I don't think they get any leverage even after 30 days.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Thanks for the update. So can you at least show a snapshot of your current portfolio, perhaps showing gain/loss? I think screen capture would be fine.

As I understand it, you now have about $50K in the mutual fund and about $50K (on margin) split 40/60 in BND/VTI, but it wasn't clear that you'd already initiated the positions, or if this is what you are planning to do.

Seems to me that since you can't buy the fund on margin, you might as well just stick with the ETFs. This would be simpler, and would eliminate the alpha variable from your experiment. Or are you attached to the alpha?

Minor detail, but when I had an IB account, they had a couple of monthly minimum fees. As I recall, $10 for access to the basic exchanges and minimum $10 in commissions, so basically minimum of $20/month. Is that still the case? If so, that adds about 0.5% annually on $50K, which is significant relative to your borrowing cost, no? Obviously this decreases as a factor as your portfolio grows.

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

Post by market timer »

Rob Bertram wrote:I need to spend more time understanding options and futures. I know that there are S&P 500 index futures which are sufficiently diverse, but I don't know of a similar bond future.
There are Treasury bond futures. You can buy those plus corporate bond and mortgage ETFs (e.g., VCLT, VCIT, MBB) to get a blend similar to BND. I prefer this approach to buying BND as it allows me to tailor duration (I tilt long duration) and credit risk. Once your account reaches $100K, I think you'll find futures preferable to other modes of implementation.
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Re: Should I use margin to buy a balanced fund?

Post by Spec7re »

You can also leverage any ETF with options by creating a synthetic position, which is buying a call option and selling put option at the same price. I'm not sure if the implied financing is as good as treasury futures, but it should still beat the margin rate.
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Re: Should I use margin to buy a balanced fund?

Post by Tanelorn »

Kevin M wrote:Minor detail, but when I had an IB account, they had a couple of monthly minimum fees. As I recall, $10 for access to the basic exchanges and minimum $10 in commissions, so basically minimum of $20/month. Is that still the case? If so, that adds about 0.5% annually on $50K, which is significant relative to your borrowing cost, no? Obviously this decreases as a factor as your portfolio grows.
The $10 minimum commissions are waived once you get to $100k now. If you're only trading very liquid things, you don't have to buy their basic exchange data package either.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Kevin M wrote:Thanks for the update. So can you at least show a snapshot of your current portfolio, perhaps showing gain/loss? I think screen capture would be fine.
Right now, it's about even, maybe down $40 as of Friday. As strange as this sounds, I'm not actually tracking my gain or loss in my spreadsheet, just my relative balance of bonds to stocks. I've added the transactions to my Google finance portfolio and have added screen shots below. Let me know if you need more information.
Image
Image
Kevin M wrote:As I understand it, you now have about $50K in the mutual fund and about $50K (on margin) split 40/60 in BND/VTI, but it wasn't clear that you'd already initiated the positions, or if this is what you are planning to do.
It's a little bit of both. It took me a couple of days to realize I couldn't buy mutual funds on margin. I added some extra cash wondering if I had to buy in 50k blocks each time. I have $66k in mutual funds now, but $14k of that is trapped in the 30-day waiting period.

I also accidentally had my spreadsheet set to 3x leverage as I was evaluating what would happen with Portfolio Margin, so I picked up too much VTI. I actually had to sell some shares as my SMA went negative. But that was just me not paying attention. Once the 30-day waiting period is up, I'll re-balance to the correct VTI/BND ratio.
Kevin M wrote:Seems to me that since you can't buy the fund on margin, you might as well just stick with the ETFs. This would be simpler, and would eliminate the alpha variable from your experiment. Or are you attached to the alpha?
I'm definitely not attached to the alpha. I do like the daily rebalancing and the concept of only having one fund, though. That removes a level of complexity. I still plan to re-balance/lever every month as I add money into the account, so maybe not much is lost with a traditional 3-fund portfolio. I do believe that the market portfolio is the efficient one, so going TSM/TISM/TBM would be ideal.

For me, the deciding factor for going with just ETFs is the 30-day wait. I started in late July, and the portfolio won't be properly assembled until the end of November. Now that I have the fund, I'll keep it until I switch to a PM account which will probably be in a year and a half. Though, I'll only be buying ETFs in the future.
Kevin M wrote:Minor detail, but when I had an IB account, they had a couple of monthly minimum fees. As I recall, $10 for access to the basic exchanges and minimum $10 in commissions, so basically minimum of $20/month. Is that still the case? If so, that adds about 0.5% annually on $50K, which is significant relative to your borrowing cost, no? Obviously this decreases as a factor as your portfolio grows.
I opted out of the data package, so I only have the $10 minimum commissions. Buying mutual funds is a flat $14.95 which is a little pricy, but I was willing to pay that for simplicity. With a 3 ETFs, it's about $1.20 per trade ($1 minimum, I believe). So that will be about $3.60 in commissions. So until I get above the $100k, I'll be paying about $120/year in commissions. That's about 120/66000 = 0.0018 or 18 basis points. It's definitely a drag on returns.

I am tempted to add another 45k to the portfolio so I can switch to PM now, but that breaks the parameters that I set up for the experiment. As it is, I bent some the rules by dumping some extra cash in September. It was the 2-month panic money plus October's (and some of November's) deposit a little early.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

market timer wrote:
Rob Bertram wrote:I need to spend more time understanding options and futures. I know that there are S&P 500 index futures which are sufficiently diverse, but I don't know of a similar bond future.
There are Treasury bond futures. You can buy those plus corporate bond and mortgage ETFs (e.g., VCLT, VCIT, MBB) to get a blend similar to BND. I prefer this approach to buying BND as it allows me to tailor duration (I tilt long duration) and credit risk. Once your account reaches $100K, I think you'll find futures preferable to other modes of implementation.
Thanks for that tip! I'll need to look at their risk profiles to see what maximum draw down will be. I still like simplicity. Though, I'm happy to make a process better once I flush out all the mechanics.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Tanelorn wrote: The $10 minimum commissions are waived once you get to $100k now. If you're only trading very liquid things, you don't have to buy their basic exchange data package either.
Interesting. So, without the data package you can't get quotes, right? I was trading options, so I couldn't see doing without the data package. At any rate, I needed the package for whatever it was I was doing.

So, without the data package you still use their trading platform application to enter orders, but just can't see quotes? Can you still create different portfolio views and things like that?

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

Post by market timer »

Kevin M wrote:Interesting. So, without the data package you can't get quotes, right? I was trading options, so I couldn't see doing without the data package. At any rate, I needed the package for whatever it was I was doing.
You can get the bid/offer on options from a different broker that doesn't charge for data.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Johno wrote:Leveraged ETF's though can be less costly than margin borrowing. The ETF's are generally doing so called total return swaps with implied borrowing rates of LIBOR+ the profit margin of the derivative provider, nowhere near 1.5% (FF+1.5% is only slightly less than L+1.5% in today's market, even for term). The cheapest of them are the 3X'ers with ER's around .9%, meaning around .3% for each 'leg'.

The cheapest way to lever, by far, though is (equity index) futures, though the most liquid are S&P 500 based (rather than TSM funds some might prefer). The futures contract price reflects an implicit borrowing rate of around LIBOR flat. And the bid/offer and commissions will only add up to around 7bp pa**. This blows the doors off margin borrowing or leveraged ETF's.
I've stayed out of this thread up to now due to the OP's request
Off topic:
- 2x and 3x leveraged ETFs. (UPRO, SSO, etc.) They don't work the same as one would want in a buy-and-hold portfolio
However its worth noting that whilst LETF's cost more to carry than Futures, the 'cash' can be tied up for longer and earn a higher return.

With futures you need immediate funds to hand in the event of a margin call. With LETF's you don't and can adjust positions in your own time.

I use 2x LETF's to replicate 1x stock exposure i.e. half as much in 2x (half in bonds) as would have been invested in 1x. Providing you rebalance that back to 50/50 once/year or so that will generally track the 1x reasonably closely. If the half in bonds earns more than what the LETF pays to 'borrow' in order to leverage, then you're up overall. Or I might hold a third in 3x, two thirds in bonds to similar effect.

Say we start with $10K of stock exposure via $5K in 2x, $5K in bonds. If stocks drop and you end up holding $3500 in 2x, $5000 in bonds $8500 total (i.e. 1x stock exposure down around 15%), then that's like holding $7000 in 1X stock and $1500 in bonds - whereas you'd want to be holding around $8500 of stock exposure (1x stock value down 15% from $10,000 to $8500). If you rebalance to a third in 3x, two thirds in bonds ($2833 3X, $5667 bonds) you're in effect holding 3 x 2833 = $8500 1X stock exposure whilst your bonds have increased from $5000 to $5667 i.e. you've increased stock exposure without having to sell bonds - that might be tied into a higher return. Had you rebalanced 2x holdings, then you'd be holding $4250 2x and $4250 bonds to provide the same $8500 of 1x stock exposure equivalent - which would have entailed reducing bond holdings down from $5000 to $4250 (sell $750 worth of bonds, perhaps incurring a early withdrawal penalty for doing so).

Later if the $5000 that was perhaps in a 1 year term bond and that matures, and assuming stock price/values remained the exact same then I might switch back to using half in 2x, half in bonds ($4250 2x, $4250 bonds) and only roll that $4250 amount into a replacement 1 year bond.

Overall I suspect the two broadly wash. Futures requiring more immediate access to 'cash' just in case of margin calls (or potentially being stopped out maybe at the worst possible time (down spike glitch)), such that the 'cash' earns a lower rate of return, or pay more for leverage - but the cash earns more through being able to be tied up rather than needing liquidity. Assuming the same overall rewards for both choices, the LETF choice is the safer as you don't have the risk of being stopped out/margin called when you're not around to immediately deal with that margin call.

Personally I like to use a 5 year bond ladder for such LETF based 1x replication as the (not marked to market) reward from a ladder is the average of the five year 5-year yields whilst you have 20% each year rolling (cash in hand) and another 20% that is 12 months from maturity and converging towards its par/face value price (I tend to have bonds maturing more frequently that yearly however, 10% cash in hand every 6 months for example).

Somewhat like comparing LIBOR+x borrowing cost for LETF's, LIBOR for futures, but where futures cash might earn T-Bill rates of return whilst LETF cash might earn the 5 year T yield return - and overall the two broadly compare in end result (tracking the stock index). What I do however is accept an element of higher risk by seeking out alternatives to a 5 year Treasury ladder, such as CD ladder that are protected (to within limits) and generally pay a higher interest rate than a 5 year T ladder. Often those bonds however lock you in for the term, so including some corporate bonds that can be immediately disposed of helps with liquidity risk. Generally that yields a higher overall reward, but does involve greater risk i.e. corporate bond default premium benefit/risk.

etfreplay is quite a good web site for comparing how half in 2x, half in bond compares to 100% 1x.

Image

Just remember that you need to rebalance once/year or so otherwise the tracking error can start to drift excessively.
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Re: Should I use margin to buy a balanced fund?

Post by market timer »

Clive wrote:Just remember that you need to rebalance once/year or so otherwise the tracking error can start to drift excessively.
Agree with you that leveraged ETFs are a fine way to implement this strategy. However, seems to me that using rebalancing bands, rather than a calendar-based frequency, would make more sense for maintaining a given level of exposure.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

I appreciate your input, Clive!

The challenge with leveraged ETFs is that they do not work the way that we want them to -- at least, not in the way that long-term buy-and-hold strategies need. Most leveraged ETFs track the daily movement of their corresponding index. (There are some that do it on a monthly basis, but I believe those are relatively new.) From what I understand, they track the daily movements very well, but daily movements compounded for a year is drastically different than holding a single share of a normal ETF for a year.

Several pages back, we discussed leveraged ETFs briefly. The problem with leveraged ETFs is that volatility reduces their effectiveness. We gave the hypothetical example of the market increasing by 10% one day then dropping by 10% the next. The net result would be that a normal ETF would drop by 1%, 2x leveraged by 4%, and 3x leverage by 9%. On the other hand, trending works in a leveraged ETF's favor.

For what it's worth, every dollar invested in SSO gives about the same long-term returns as SPY. Sure, there are higher returns but even higher risk. After costs are considered, SPY is the better bet as it has a slightly higher Sharpe ratio:

Code: Select all

Risk measurement               ProShares Ultra S&P500 (SSO)    SPDR S&P 500 ETF (SPY)
Standard Deviation (3-year)           21.39                         10.54
Sharpe Ratio (3-year)                  1.91                          2.01
Standard Deviation (5-year)           26.89                         13.17
Sharpe Ratio (5-year)                  1.07                          1.16
Image

And just to drive the point home, if you used SPY instead of SSO, the balanced portfolio would have done significantly better.
Image

In my humble opinion, I believe that leverage has a place in a long-term investment strategy, but leveraged ETFs as they are now do not fit. Maybe the monthly LETFs are better able to track the annual index performance.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

market timer wrote:
Clive wrote:Just remember that you need to rebalance once/year or so otherwise the tracking error can start to drift excessively.
Agree with you that leveraged ETFs are a fine way to implement this strategy. However, seems to me that using rebalancing bands, rather than a calendar-based frequency, would make more sense for maintaining a given level of exposure.
Yes that is more appropriate, I suggested yearly to highlight that you don't have to rebalance that often to maintain reasonable tracking. There tends to be some drift the further the weighting shifts away from 50/50 (for 2x, 33.3/66.7 for 3x) and triggering a closure of that weighting drift at rebalance bands trigger levels is more likely to keep on top of that.

I tend to look at rebalancing whenever a bond matures (cash in hand) and have bonds maturing at 6 monthly intervals. If any adjustments are small I don't bother, otherwise I adjust and reinvest the remainder back into bonds.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Rob Bertram wrote:Several pages back, we discussed leveraged ETFs briefly. The problem with leveraged ETFs is that volatility reduces their effectiveness. We gave the hypothetical example of the market increasing by 10% one day then dropping by 10% the next. The net result would be that a normal ETF would drop by 1%
And half as much in a 2x (assuming the other half of asset (bonds) has low volatility) combined, will have around the same volatility as the 1x, and in combination will gain/lose around the same as the 1x. You're comparing same amounts invested in both choices (1x and 2x), I'm looking at half as much in 2x as in 1x, which levels them.

I can assure half in 2x stocks, half in bonds will track 100% in stocks reasonably over months/years as I've been using such for years and measure my results relative to the non leveraged equivalents in total net of costs and taxes terms - and for me LETF's are a no-brainer preferred choice . As the weightings drift to perhaps 40/60 2x/bonds or 60/40 2x/bonds you will start to see some tracking error, so just don't let the weightings widen that far and periodically rebalance back to 50/50 2x/bonds.

Of sorts, the LETF fund manager takes your deposit with them and borrows the same amount again and invests the combined amount in the target stocks. If the other half that you didn't deposit with the fund manager but invested in bonds instead yields a higher reward than what the fund manager pays to borrow, then overall you'll see a higher reward. Not as simple as that as some LETF's use swaps or derivatives or whatever, but conceptually much the same.

Just a case of whether you can achieve a higher reward than what it costs to borrow, if you can you win, if you don't you lose, and where the cost to borrow is determined by whatever means the LETF manager chooses to borrow by.

Typically for 3UKL for instance (UK stock 3x) if the bond two-thirds is invested in a 5 year gilt (treasury) ladder, you'll see similar results as having invested 100% in the stocks (non leverage). So if bond yield > 5 year gilt ladder rewards then overall you tend to better the index. In the UK in February for instance 5 year gilts were priced to a 1.75% yield whilst a First Save bank cash deposit 5 year bond could be bought for 3.25% yield. That's state guaranteed (protected) up to around $140K invested - so just don't deposit any more into that bond/bank than that $140K safe amount (hold other banks bonds instead to scale up that protected amount). And/or you can typically buy 5 year corporate bonds that yield more than 5 year Treasury - but that does entail default etc risks - but can be liquidated quickly.

Distils down to rather than trying to beat the index by holding mostly index plus some sideline individual stocks that you think might outperform the index, that instead you try to beat the index via beating the cost of borrowing. Of the two I find that latter to be the easier to achieve. With stocks its a guess, with bonds you know exactly what bonds will pay when held to maturity so its just a simple calculation.
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Re: Should I use margin to buy a balanced fund?

Post by market timer »

Clive wrote:I can assure half in 2x stocks, half in bonds will track 100% in stocks reasonably over months/years as I've been using such for years and measure my results relative to the non leveraged equivalents in total net of costs and taxes terms - and for me LETF's are a no-brainer preferred choice .
On page 2 of this thread, Park provides a link to a helpful paper on this topic: http://www.etf.com/publications/journal ... funds.html

From that paper:
Rebalancing is an effective tool for investors whose goal is to approximate the daily leverage target over time. The process is straightforward and involves monitoring index returns versus fund returns and establishing a trigger percentage of deviation as a basis for the rebalancing strategy.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

An additional benefit for me as a UK investor in US stock (S&P500) is that if I buy SPY then as the trailing 12 month dividend yield is around 1.9% the US will withhold 15% of that, leaving a net 1.62% dividend, a overhead/cost of 0.28%. If instead I invest half as much is SSO and hold UK bonds for the other half, as SSO dividend yield is 0.23% then the overhead/cost reduces to 0.035% due to withholding tax. The expense ratio is higher for SSO however, 0.9% so with 50% weighting to that = 0.45%, add on the 0.035% and the total 'cost' is around 0.485%. A S&P500 tracker (Vanguard perhaps) might have a expense ratio of 0.07%, but incurs 0.23% withholding tax for a total 'cost' of 0.3%. So half in 2x, half in bonds is a little more expensive (0.15%), however I have the opportunity to recoup that (and more) should the bond half do OK. If bonds earn 1% more than the cost of borrowing that the LETF incurs, then = 0.5% weighted benefit, which eliminates the 'costs'. Rather than lagging the gross total return index by 0.3% for the least expensive choice (Vanguard), total actual rewards are comparable to that gross total index return - plus some.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

market timer wrote:On page 2 of this thread, Park provides a link to a helpful paper on this topic: http://www.etf.com/publications/journal ... funds.html

From that paper:
Rebalancing is an effective tool for investors whose goal is to approximate the daily leverage target over time. The process is straightforward and involves monitoring index returns versus fund returns and establishing a trigger percentage of deviation as a basis for the rebalancing strategy.
I've found that rotating between the various choices, all in 1x, half in 2x, third in 3x and monitoring their relative performance opens up the potential to add value by timing rotations. Sometimes I see a -4% or more drift being apparent, other times a +4% or more drift, and I treat that like premium/discount to NAV to rotate into one or another choice, holding that until the situation reverses. Nothing mathematical about that, so any benefits might be attributed to luck. However I've found I've been quite lucky on that front and timing has added more benefits than the benefits from my choice of bonds. Typically that luck has added around 2% year.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Clive wrote:
Rob Bertram wrote:Several pages back, we discussed leveraged ETFs briefly. The problem with leveraged ETFs is that volatility reduces their effectiveness. We gave the hypothetical example of the market increasing by 10% one day then dropping by 10% the next. The net result would be that a normal ETF would drop by 1%
And half as much in a 2x (assuming the other half of asset (bonds) has low volatility) combined, will have around the same volatility as the 1x, and in combination will gain/lose around the same as the 1x. You're comparing same amounts invested in both choices (1x and 2x), I'm looking at half as much in 2x as in 1x, which levels them.
So the first major thing to understand is that the annualized returns of SSO are not 2x of SPY despite being a 2x leveraged ETF. The Morningstar graph that I posted demonstrates that. If you invested $1 in SSO and $1 in SPY on the day that SSO was available, then you would have roughly the same in SSO and SPY today. The risk-adjusted returns are roughly the same. That's why the Sharpe ratio is relevant. It tells us that SSO gives us no long-term benefit over SPY.
Clive wrote:I can assure half in 2x stocks, half in bonds will track 100% in stocks reasonably over months/years as I've been using such for years and measure my results relative to the non leveraged equivalents in total net of costs and taxes terms - and for me LETF's are a no-brainer preferred choice . As the weightings drift to perhaps 40/60 2x/bonds or 60/40 2x/bonds you will start to see some tracking error, so just don't let the weightings widen that far and periodically rebalance back to 50/50 2x/bonds.
I think that this is where you are getting confused. Modern portfolio theory tells us that a balanced portfolio of stocks and bonds will have better risk-adjusted returns than an all-stock portfolio. That's the diversification and rebalancing "free lunch." You're then increasing your risk by picking SSO so that returns are similar to an all stock portfolio. You think that the leverage is giving you the efficiency, but it's the diversification and rebalancing that is.

Please run as many backtests as you can. Pick your favorite portfolio with SSO, then replace it with SPY and compare the results. The portfolio with SPY is more efficient long-term (i.e., it has the higher Sharpe ratio). I expect that it will have similar if not better returns and significantly lower risk.

LETFs work as expected in the short-term. If you can predict short-term movements in the market, then you can capture the movement better with LETFs. However, they lose their utility the longer that they are held due to volatility. I'm not smart enough to look at and understand short-term market behavior, so I'll stick with the long-term buy-and-hold strategy.

Now you say that taxes complicate the situation. Perhaps there is a more appropriate domestic fund that that has similar performance.
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Re: Should I use margin to buy a balanced fund?

Post by Clive »

Rob Bertram wrote:Please run as many backtests as you can. Pick your favorite portfolio with SSO, then replace it with SPY and compare the results. The portfolio with SPY is more efficient long-term (i.e., it has the higher Sharpe ratio). I expect that it will have similar if not better returns and significantly lower risk.
Can't get nicely formatted table data, but for 50% SSO, 50% IEI yearly rebalanced (sourced from etfreplay) :-

Columns :
Year
SSO/IEI 50/50 Total Return
SPY Total return
SSO/IEI Volatility
SPY Volatility

2008 -27.8 -36.8 21.2 41.3
2009 22.8 26.4 24.2 26.6
2010 16.6 15.1 16.4 18
2011 2.7 1.9 20.4 23
2012 16.4 16 13.4 12.7
2013 34.3 32.3 12.4 11.1
YTD 2014 8.2 7.9 9.9 10.2

Averages
10.46 SSO/IEI yearly gain
8.97 SPY yearly gain
16.84 SSO/IEI yearly volatility
20.41 SPY yearly volatility

Total compound gain over the 6.83 years
79.6% SSO/IEI
55.1% SPY

SSO/IEI had a higher average (10.46%) than SPY (8.97%)
and a lower average volatility (16.84%) than SPY (20.41%)
SSO/IEI had a higher compound gain (79.6%) than SPY (55.1%)
8.95% annualised (SSO/IEI) versus 6.6% annualised (SPY).

Standard deviation of those yearly gains 19.7 (SSO/IEI) versus 22.7 (SPY)

Without calculating the actual Sharpe, pretty sure it was better for SSO/IEI than for SPY over those 6.8 years.

The proof of the pudding is in the eating and I know which pudding I prefer to eat.
Topic Author
Rob Bertram
Posts: 859
Joined: Mon May 05, 2014 12:15 pm

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

Post by Rob Bertram »

I'm agreeing with you that a balanced portfolio of stocks and bonds is more efficient than an all-stock portfolio. That's the premise of my argument for leveraging a balanced portfolio instead of just leveraging stocks.

What I'm saying is that your SSO/bond portfolio should be compared to SPY/bond and not just to SPY/nothing. In the recent past, bonds performed better than stocks, so it stands to reason that a bond-heavy portfolio would perform better than a stock-only portfolio. Below is an example of what I mean. The first graphic is of the SSO/IEI portfolio. The second is with SPY instead of SSO but with everything else the same. The portfolio with SPY performed better than SSO despite SSO being a 2x leverage ETF.

Image
Image
Clive
Posts: 1950
Joined: Sat Jun 13, 2009 5:49 am

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

Post by Clive »

Rob Bertram wrote:What I'm saying is that your SSO/bond portfolio should be compared to SPY/bond and not just to SPY/nothing. In the recent past, bonds performed better than stocks, so it stands to reason that a bond-heavy portfolio would perform better than a stock-only portfolio.
A fairer comparison would be :

SSO/IEI 25/75 compared to SPY/IEI 50/50

Code: Select all

2008	-7.4	-12
2009	10.5	12.3
2010	11.4	10.7
2011	5.5	 5.1
2012	9.1	 8.9
2013	16.2	15.2
YTD	 5.2	 5
60.4% compound gain compared to 51.5%

Also, if you don't rebalance yearly then you will see deviations i.e. after the 2008 declines SSO would have become a relatively small weighting relative to bonds.

Think of a any target allocation to SPY = x% and the remainder to bonds (IEI), and instead allocate x/2 % to SSO and the remainder to IEI and test yearly gains (so once yearly rebalanced back to target weightings) and generally overall you'll tend to see better results using SSO. Simply because on average 50% SSO/50% IEI tends to be >100% SPY. Typically because what SSO pays to borrow is less than what IEI earns..
Clive
Posts: 1950
Joined: Sat Jun 13, 2009 5:49 am

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

Post by Clive »

Try this line of thought Rob.

A fictitious leveraged ETF takes the money you invest with them and borrows the same amount again and buys 2x exposure of the index that they track, readjusting daily. You invest 0.5 in that fund, 0.5 in a charitable bank that pays you the exact same interest on deposits as what it charges to lend to the LETF manager. Overall, other than trading costs that's zero sum, no different to had you just directly invested all 1 in the index.

A 30% down year for stocks is a bad year. With 0.5 in stocks, 0.5 in bonds at year end after such a decline you might be holding 0.1 in 2x, 0.6 in bonds, combined 0.7 which reflects the 30% decline in 1x. To rebalance back to 50/50 weighting you might adjust to 0.35 2x, 0.35 bonds. OR you might adjust to 0.23 3x, 0.52 bonds (third in 3x, two thirds in bonds). Note however under such conditions the amount of bonds rose from 0.5 to 0.52 and as such you didn't need to sell any bonds (but rather added to them) after such a decline in stock prices.

Which means you can tie your bonds up for longer, potentially with those bonds paying a higher interest rate. If each year I bought a 5 year CD bond that paid 3.25%, but locked you in for the term (no early redemption) then that's a reasonable premium relative to 1.75% 5 year treasury bonds (I'm using UK figures here as of last February). A ladder of such bonds will have one maturing each year, 20% of bonds becoming available as cash in hand, which might be redirected towards adding more stock exposure (or reducing the amount of leverage (perhaps down from using a third in 3x, two thirds in bonds to using half in 2x, half in bonds).

Unlike institutes/funds those CD bonds might be Fed (or whatever) insured, so you're yielding more, for no extra risk. And more often that structure will yield more than what the LETF pays to borrow.

Also note with yearly rebalancing the most the LETF can lose is 100% of its value, but if you'd started the year with 50/50 of LETF/bonds you'll still have the 50% bond value remaining. So if stocks dived 70% you might end up with a original 0.5 in 2x, 0.5 in bonds being left with 0.0 2x and 0.5 in bonds. As one rung of a 5 year bond ladder matures, you might adjust to holding 0.1 in 3x, 0.4 in bonds.

By avoiding margin calls and potentially earning more than what LETF's pay to borrow, and having state backed protection of the bond value, overall you can achieve a greater reward than had you solely invested in 1x stock alone. Note however that you shouldn't have all of bond tied into fixed term (no early redemption/exist) as there are some cases where a degree of liquidity could be required. 4 rungs of the ladder in fixed term (non early redeemable), one more liquid rung would generally suffice.

Rather than having a 5 year ladder with one bond maturing once every year, holding 10 bonds with 6 months between maturing bonds is an alternative choice (or any other sub-division).

This is a very similar to what Johno outlined back on page 2 of this thread - except it mitigates margin call (liquidity) risk.

Hope this helps.

Clive.
Topic Author
Rob Bertram
Posts: 859
Joined: Mon May 05, 2014 12:15 pm

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

Post by Rob Bertram »

I think that there are two critical aspects that you are missing.
1) Daily returns leveraged does not equal annual returns leveraged. Volatility reduces this. The larger the swing, the larger the loss. A good year to look at is 2011. The S&P returned about 1.9%, but SSO lost about 3.9%. It missed the 2x annual returns by about 8% (expected +4% but got -4%). You can see this even better if you combine SSO (+2x S&P500) with SDS (-2x S&P500). Conceptually, these should net to 0 as they are tracking the same index. This is the mental zero sum that you're doing by putting half in SSO and half in a bank. Instead of returning 0% as one would expect from the zero sum, a 50/50 portfolio of SSO and SDS lost about -10.9%.

Below is the SSO/SDS portfolio. For the first half of the year, volatility is relatively low, and the portfolio is fairly flat. For the last half of the year, volatility skyrockets, and the portfolio trends down in practically a straight line.
Image

In a traditional buy and hold strategy, when a stock value drops, we hold our position. If it drops enough to trigger a rebalance, we buy more. A leveraged ETF on the other hand sells assets to meet its debt obligations when its value drops and buys more assets when its value increases daily. Remember that 10% swing example that I gave? With a 10% drop/gain, an unleveraged asset loses 1%, 2x leveraged loses 4%, and 3x loses 9%. What about a 18.61% swing which is what happened in 2011? I'll round it to 20% to make the math easy -- 4% (unleveraged), 16% (2x), 36% (3x). Even if you hold 1 share of SSO and don't sell, its value is significantly less as it sold off 16% of its assets.

2) Your balanced portfolio of SSO and bonds does better despite the leverage not because of it. Modern Portfolio Theory and rebalancing tell us that we get better risk adjusted returns by selling higher performing assets and buying lower performing assets. Leveraged ETFs do the exact opposite. Holding SPY instead of SSO will give you better risk adjusted returns. And, in the long-term, SPY should perform better. I've done all that I can to show you that. I showed you Sharpe ratios. I showed you the Morningstar chart. I showed you similar balanced portfolios on ETF Replay.
Clive wrote:
Rob Bertram wrote:What I'm saying is that your SSO/bond portfolio should be compared to SPY/bond and not just to SPY/nothing. In the recent past, bonds performed better than stocks, so it stands to reason that a bond-heavy portfolio would perform better than a stock-only portfolio.
A fairer comparison would be :

SSO/IEI 25/75 compared to SPY/IEI 50/50
No, a fair comparison would be SSO/IEI 50/50 vs SPY/IEI 50/50. (I already posted the ETF Replay charts.) Like I said in the part that you quoted, bonds performed better than stocks. Increasing the bond percentage is hiding the underperformance of SSO.

And returns are only half of the picture, you also need to look at risk. There are some periods where SSO had higher returns than SPY, but there aren't as many as one would hope considering that SSO is 2x levered and the recent bull market. And you're taking on more risk than the return justifies.

So here's a risk-adjusting exercise for you to try:
  1. Pick your favorite portfolio with SSO and any mix of bonds/cash. Call this Portfolio A. Record the returns and the volatility (standard deviation).
  2. Take that same portfolio and replace SSO with SPY. Keep everything else including asset allocation the same. Call this Portfolio B. Record the returns and volatility.
  3. Lever Portfolio B so that it has the same risk as Portfolio A. Assume 1.5% cost of borrowing. Call this Portfolio C.
  4. The risk of Portfolio A is the same as Portfolio C by the way we constructed it. Which portfolio has higher returns?
I will do this for the SSO/IEI 50/50 portfolios that I posted above.
Portfolio A: SSO / IEI 50/50: Returns (CAGR): 5.2%, risk = 12.3%
Portfolio B: SPY / IEI 50/50: Returns (CAGR): 5.7%, risk = 8.1%
Portfolio C: Leverage factor = 12.3/8.1 = 1.5, Returns (CAGR): 5.7 *1.5 - (0.5 * 1.5) = 7.8%.

Adjusting for risk, the SPY portfolio gave 7.8/5.2 = 1.5 x higher returns than the SSO portfolio.
Clive
Posts: 1950
Joined: Sat Jun 13, 2009 5:49 am

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

Post by Clive »

Rob Bertram wrote:I think that there are two critical aspects that you are missing.
1) Daily returns leveraged does not equal annual returns leveraged.
...
No, a fair comparison would be SSO/IEI 50/50 vs SPY/IEI 50/50
The LETF's clearly indicate that they do not leverage to twice the annual return, but typically twice the daily move i.e. twice the VOLATILITY. I have never suggested that a 2x LETF will provide twice the yearly gain (loss) of the 1x.

Comparing equal weightings of one asset that is twice as volatile as another is a somewhat meaningless comparison. Its better to use a risk parity based comparison and level the volatility (half as much in the 2x as in the 1x). Also you shouldn't compare multiple years as likely the weightings would have deviated away from 50/50 (or whatever proportions). Otherwise you'll get all sorts of complications set in

2013 SSO/IEI 50/50 gain = 34.3 volatility = 12.4, Pythagorean CAGR approximation = 33.7%
2013 SPY/IEI 50/50 gain = 15.2 volatility = 6.0 Pythagorean CAGR approximation = 15%

33.7 / 15 > 2

Image

Better IMO to

Arbitrarily pick any SPY/IEI weighting : 34/66
Arbitrarily pick a single year : 2011
etfreplay indicates 6.1% gain with 6.4% volatility

Half as much in SSO as SPY = 17/83 weightings and for the same year
etfreplay indicates 6.4% gain wth 5.3% volatility

Perhaps that was down to a higher weighting of bonds, so switching to
66/34 SPY/IEI = 4.1% gain with 14% volatility
33/67 SSO/IEI = 4.6% gain with 12.5% volatility

I've been using LETF's for over 5 years now to good effect in practice with not insignificant amounts of real money, so perhaps best left as a begging to differ disagreement Rob.

Best wishes. Clive.
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market timer
Posts: 6535
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Re: Should I use margin to buy a balanced fund?

Post by market timer »

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).

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.

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.
lee1026
Posts: 396
Joined: Sat Jun 21, 2014 7:47 pm

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

Post by lee1026 »

There is a few other concerns on leveraging S&P 500 via either SPY, SSO or e-mini. If you use SPY, you owe taxes on any gains only when you sell. If you are selling to reduce your exposure and leverage after a crash, then by definition you lost money and don't owe taxes. If you use SSO and desire a leverage smaller then 2x, then you need to sell as it goes up, leaving you with tax bills. If you use e-minis, you get to pay taxes on all gains.

Based on this, I would only leverage via SPY, even though IB's interest rates is way higher then the implicit borrowing rates elsewhere.

For Rob though, there is no tax advantage to use ETFs for bonds instead of futures. (Indeed, using ETFs for futures will produce bigger tax bills!!), so I would suggest just buying a ton of SPY and bond futures.
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