A levered 50/50 portfolio is better than a 90/10 one?

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Day9
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A levered 50/50 portfolio is better than a 90/10 one?

Post by Day9 »

According to Modern portfolio theory, it could be better (more reward with less risk) to have a leveraged 50/50 portfolio than a 90/10 unlevered portfolio, depending on the cost of leverage and the covariance between stocks and bonds.

Would someone be able to demonstrate a sample, hypothetical cost of leverage and correlation between stocks and bonds that would yield that under MPT the levered 50/50 portfolio would be better than the 90/10 one?

If it helps to assume these simple and close enough metrics than please do so.

Stocks:
Return = 10%
Standard Deviation = 20%

Bonds
Return = 5%
Standard Deviation = 5%

Cheers.
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stemikger
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by stemikger »

Day9 wrote:According to Modern portfolio theory, it could be better (more reward with less risk) to have a leveraged 50/50 portfolio than a 90/10 unlevered portfolio, depending on the cost of leverage and the covariance between stocks and bonds.

Would someone be able to demonstrate a sample, hypothetical cost of leverage and correlation between stocks and bonds that would yield that under MPT the levered 50/50 portfolio would be better than the 90/10 one?

If it helps to assume these simple and close enough metrics than please do so.

Stocks:
Return = 10%
Standard Deviation = 20%

Bonds
Return = 5%
Standard Deviation = 5%

Cheers.
This is what Warren Buffett says about leverage:

If you’re smart, you don’t need leverage. If you’re dumb, you have no business using it.
Choose Simplicity ~ Stay the Course!! ~ Press on Regardless!!!
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by YDNAL »

Day9 wrote:According to Modern portfolio theory, it could be better (more reward with less risk) to have a leveraged 50/50 portfolio than a 90/10 unlevered portfolio, depending on the cost of leverage and the covariance between stocks and bonds.

Would someone be able to demonstrate a sample, hypothetical cost of leverage and correlation between stocks and bonds that would yield that under MPT the levered 50/50 portfolio would be better than the 90/10 one?
Your first paragraph reaches an apparent conclusion.... "According to MPT it could be better..."

The second paragraph asks others to *hypothetically* demonstrate (prove) if this can be the case.

Personally, I manage our Income Statement AND Balance Sheet - where *DEBT* and its cost is a sure/known thing. *Hoped-for* returns are not.
Landy | Be yourself, everyone else is already taken -- Oscar Wilde
grayfox
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by grayfox »

Suppose there are two random variables, X and Y with mean mu, standard deviation sigma and variance sigma^2
Correlation rho.XY and covariance cov(X,Y) = sigma.XY = rho.XY / sigma.X * sigma.Y
For the example, assume correlation is zero.

Code: Select all

mu.X		0.1
Sigma.X	0.2
Sigma2.X	0.04
		
mu.Y		0.05
Sigma.Y	0.05
Sigma2.Y	0.0025

Rho.XY	0	0
Sigma.XY	0	0

Z is a linear combination of X and Y, 100% invested, a + b = 1, and no shorts, a,b >= 0

Code: Select all

Z = aX + bY
b = 1 - a
The mean, standard deviation, and Sharpe slope of Z is, assuming risk-free rate = 0
Mean is just weighted average, mu.Z = a*muX + b*muY
Variance is more complicated. Sigma2.Z = a^2*sigma2.X + b^2*sigma2.Y + 2ab*sigma.XY

Code: Select all

     50/50    90/10
a	0.5	0.9
b=1-a	0.5	0.1

mu.Z	0.075	0.095

a^2*sigma2.X	0.010	0.032400
+ b^2*sigma2.Y	0.001	0.000025
+ 2ab*sigma.XY	0.000	0.000000		
= Sigma2.Z		0.011	0.032
Sigma.Z	0.103	0.180

Sharpe Slope	0.7276	0.5276
Sharpe slope = ( mu.Z - rf ) / sigma.Z, or if rf = 0, then mu.Z / sigma.Z

50/50 has higher Sharpe slope than 100/0, 0.728 vs. 0.500. Assuming that you can borrow at the risk-free rate, if you leverage up the 50/50 1.27:1, it will have the same return as the 90/10, but at a lower standard deviation.

Code: Select all

Leverage	1.27	1.00
Expected Ret	0.0950	0.0950
SD	0.1306	0.1801
You can move along the line by borrowing or lending at the risk-free rate. The Sharpe slope is the slope of the line, and the y-intercept is the risk-free rate.

Image

Now if you can't borrow at the risk-free rate, don't blame me. Bring it up with Bill Sharpe. It's called Modern Portfolio Theory.
Last edited by grayfox on Sat Nov 23, 2013 3:47 pm, edited 2 times in total.
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Day9
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Day9 »

Thanks grayfox for your thoughtful reply that was not just a thoughtless platitude.
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YDNAL
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by YDNAL »

Day9 wrote:Thanks grayfox for your thoughtful reply that was not just a thoughtless platitude.
There were 2 responses prior to grayfox, one being my response.
  • To reiterate, I believe in managing our personal Income Statement and Balance Sheet. So, adding debt in order to increase assets means strict focus on the Income Statement. This is fact!!
  • Can you expand on the need (and basis) for your parting comment ?
Landy | Be yourself, everyone else is already taken -- Oscar Wilde
Rodc
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Rodc »

Day9 wrote:Thanks grayfox for your thoughtful reply that was not just a thoughtless platitude.
Note well that grayfox's response neglected both the cost and extra risks of leverage (not just market type risk but things like call risk).

The specifics of precisely how you obtain the leverage will be needed in order to assess these factors. It would be very unusual for the final expected return and risk of a levered portfolio to beat an unleveraged one, though in some cases you might be able to do so.

There are good reasons why advice to use leverage is so rare.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by G-Money »

Which is better will really depend on cost of leverage.

Leverage is borrowing. Investing in bonds is lending. So, really, one offsets the other.

Say you start with $100,000 in assets.

You can invest it 90/10, which would give you $90,000 in stocks and $10,000 in bonds.

Or, in your other proposal, you could borrow (leverage) an additional $80,000 (bringing your investable assets to $180,000) to allocate in a 50/50 portfolio. So you would have $90,000 in stocks, $90,000 in bonds, and -$80,000 in debt. Since your leverage can be viewed as a "negative bond,"* your asset allocation is really $90,000 stocks and ($90,000 bonds - $80,000 debt = $10,000 bonds).

So, assuming you are not subject to margin calls and assuming the interest rates for bonds and debt are the same, the two proposals are equivalent. They would have the same expected return.

Where this breaks down in practice is that retail investors can rarely borrow at the same terms at which they can lend. If you are investing on margin in a brokerage account, there will almost certainly be margin call provisions. And nearly all borrowing options will entail higher borrowing costs. Compare mortgage/home equity rates (including closing costs) to comparable Treasuries.


* http://www.bogleheads.org/wiki/Owning_v ... e_bonds.29
http://www.bogleheads.org/wiki/Paying_d ... _investing
Don't assume I know what I'm talking about.
Texas hold em71
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Texas hold em71 »

YDNAL wrote:
Day9 wrote:According to Modern portfolio theory, it could be better (more reward with less risk) to have a leveraged 50/50 portfolio than a 90/10 unlevered portfolio, depending on the cost of leverage and the covariance between stocks and bonds.

Would someone be able to demonstrate a sample, hypothetical cost of leverage and correlation between stocks and bonds that would yield that under MPT the levered 50/50 portfolio would be better than the 90/10 one?
Your first paragraph reaches an apparent conclusion.... "According to MPT it could be better..."

The second paragraph asks others to *hypothetically* demonstrate (prove) if this can be the case.

Personally, I manage our Income Statement AND Balance Sheet - where *DEBT* and its cost is a sure/known thing. *Hoped-for* returns are not.

I do the same as you YDNAL, but MPT does not really support it. A good economist will make some estimate about realistic returns and not assume zero. And a good economist will know that leverage increases both return and risk.

Because of my behavioral bias, I focus only on the risk and therefore miss some of the excess return. I think OP is trying to find the mathematical breakpoint for himself. Is it better to lever on 50/50 or hold 90/10? You and I would choose neither.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Rodc »

G-Money wrote:Which is better will really depend on cost of leverage.

Leverage is borrowing. Investing in bonds is lending. So, really, one offsets the other.

Say you start with $100,000 in assets.

You can invest it 90/10, which would give you $90,000 in stocks and $10,000 in bonds.

Or, in your other proposal, you could borrow (leverage) an additional $80,000 (bringing your investable assets to $180,000) to allocate in a 50/50 portfolio. So you would have $90,000 in stocks, $90,000 in bonds, and -$80,000 in debt. Since your leverage can be viewed as a "negative bond,"* your asset allocation is really $90,000 stocks and ($90,000 bonds - $80,000 debt = $10,000 bonds).

So, assuming you are not subject to margin calls and assuming the interest rates for bonds and debt are the same, the two proposals are equivalent. They would have the same expected return.

Where this breaks down in practice is that retail investors can rarely borrow at the same terms at which they can lend. If you are investing on margin in a brokerage account, there will almost certainly be margin call provisions. And nearly all borrowing options will entail higher borrowing costs. Compare mortgage/home equity rates (including closing costs) to comparable Treasuries.


* http://www.bogleheads.org/wiki/Owning_v ... e_bonds.29
http://www.bogleheads.org/wiki/Paying_d ... _investing
+1

Excellent explanation.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by stlutz »

Since the weather isn't that great where I live today...

I pulled up the Simba spreadsheet and ran some numbers from 1972 through 2012. To get the same portfolio standard deviation as the 90/10 portfolio, I ended up levering the 50/50 portfolio by 62%. I also charged myself margin interest.

My end result was that the 90:10 portfolio returned 9.77% per year. To equal that return, my borrowing costs had to be 1.75%.

On a hypothetical $100,000 portfolio, one can borrow at interactive brokers for 1.59%. So, you could come out ahead by .16% per year if you assume that margin calls never happen.

My conclusion: A levered 50/50 portfolio is not better than a 90/10 one.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

If one wants cheap leverage, they can always use futures. It is cheaper than Interactive Brokers margin interest.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Clive »

Assuming you invested 50% in SSO (2x SPY ETF) and 50% in TIP ETF each year, then compared to 100% SPY, total gains (dividends etc included) and volatility figures (from etfreplay.com) indicate :

Gain Volatlity
2007
SSO/TIP 6.5 14.7
SPY 5.1 15.9

2008
SSO/TIP -34.2 24
SPY -36.8 41.3

2009
SSO/TIP 28.1 24.6
SPY 26.4 26.6

2010
SSO/TIP 16.5 17.2
SPY 15.1 18

2011
SSO/TIP 5.2 19.5
SPY 1.9 23

2012
SSO/TIP 18.7 13.1
SPY 16 12.7

Most years had a higher gain from 50/50 with a lower volatility (better risk adjusted reward (Sharpe)).

Compounded total gain over all of those years = +30.6% for the 50/50 versus +14.2% for SPY.

Leveraged ETF's rebalance daily, which has the effect of increasing exposure during up-trends, reducing exposure during down-trends. Hence 2008 crisis saw the 50/50 down less and the 2009 rebound up more.

There are different risk factors involved, counter-party etc. But equally there are risk reductions involved. If 50% in 2x ETF, 50% in TIPS sees the ETF wiped out for whatever reason, your loss is limited to the 50% amount invested rather than a 100% loss for instance had you been fully loaded in an ETF that was wiped out.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by nisiprius »

I don't think it is right to say it is "Modern Portfolio Theory" that predicts this. You don't need MPT at all.

It is a truism that for any portfolio whatsoever, you can always increase its expected return by using leverage. Nothing to do with MPT, it's just what leverage does, plain and simple.

MPT assumes that everyone understands that you can move up and down at will along the straight line between the portfolio and the riskless asset. The question that it tries to answer is to find the best mix of the high-earning assets. It assumes that after you have located that best mix, you will either dilute it or possibly leverage it with the riskless asset in order to reach your desired level of risk. And if you start with the tangency profile and someone else starts with a non-tangency profile, then for any desired standard-deviation "risk," you will have a higher return than they will.

A problem with the consideration of leverage is that simple calculations--such as extrapolating lines on charts--make an implicit assumption that you can always get however much credit you need. Of course, if you have a truly unlimited line of credit, all sorts of miraculous things become possible. For example, gambling systems such as martingales actually work, and you can win steadily at a casino, despite the house percentage being against you, "simply" by doubling up your bet then adding a bit to it, whenever you lose. The right conclusion to draw from this is not that miracles are possible, and not that you can win against a casino, but that infinite lines of credit don't exist. Unfortunately many people make the mistake of assuming that if an infinite line of credit can work miracles, then a really big line of credit can work miracles.

Once you assume that credit is limited, the possibility of financial ruin enters the picture. But MPT doesn't take this into account.

In real life, if you and I have the same standard-deviation "risk," and you have a higher return, and your portfolio has leverage but mine doesn't, then we will have the same standard-deviation "risk," but you will have a higher chance of ruin, higher "black swan" risk, higher fragility.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Rodc »

Compounded total gain over all of those years = +30.6% for the 50/50 versus +14.2% for SPY.
All those years? Six years means...?

A more fair comparison might also be had by using total bond which would not come out nearly as well.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by JoMoney »

nisiprius wrote:...infinite lines of credit don't exist. Unfortunately many people make the mistake of assuming that if an infinite line of credit can work miracles, then a really big line of credit can work miracles...
It would seem to exist if you're considered "too big to fail", but maybe that's a different topic. I don't think any of us will have the Fed drop a few billion onto our balance sheets if our portfolio scheme doesn't pan out the way historical numbers made it look.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

nisiprius wrote: In real life, if you and I have the same standard-deviation "risk," and you have a higher return, and your portfolio has leverage but mine doesn't, then we will have the same standard-deviation "risk," but you will have a higher chance of ruin, higher "black swan" risk, higher fragility.
All those are big words, with out numerical example it is just that.

Most of the people use leverage in wrong way or over levered which gives leverage bad name.

It is better to lever low volatility asset and combine with negatively correlated asset. It usually has better sharpe ratio.

I disagree with terms of credit are bad for individual traders compared to big firms.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by grayfox »

I was going out the door when I typed my original response. I went back and edited it with more explanation.

http://www.bogleheads.org/forum/viewtop ... 2#p1863552
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Rodc »

Ranger wrote:
nisiprius wrote: In real life, if you and I have the same standard-deviation "risk," and you have a higher return, and your portfolio has leverage but mine doesn't, then we will have the same standard-deviation "risk," but you will have a higher chance of ruin, higher "black swan" risk, higher fragility.
All those are big words, with out numerical example it is just that.

Most of the people use leverage in wrong way or over levered which gives leverage bad name.

It is better to lever low volatility asset and combine with negatively correlated asset. It usually has better sharpe ratio.

I disagree with terms of credit are bad for individual traders compared to big firms.
All those little words and yet not one numerical example. (Just saying...)
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by berntson »

stemikger wrote: This is what Warren Buffett says about leverage:

If you’re smart, you don’t need leverage. If you’re dumb, you have no business using it.
Eh? From what I understand, a large part of Buffet's success has been from using cheap leverage well. See this for example. Among other things, he seems to have landed on the strategy of betting against beta (improving returns by leveraging low volatility assets instead of buying higher volatility assets) before it was known in the academic literature.
Berkshire Hathaway has realized a Sharpe ratio of 0.76, higher than any other stock or
mutual fund with a history of more than 30 years, and Berkshire has a significant alpha to
traditional risk factors. However, we find that the alpha becomes insignificant when
controlling for exposures to Betting-Against-Beta and Quality-Minus-Junk factors.
Further, we estimate that Buffett’s leverage is about 1.6-to-1 on average. Buffett’s returns
appear to be neither luck nor magic, but, rather, reward for the use of leverage combined
with a focus on cheap, safe, quality stocks
Maybe his point is that if you're smart, you can do well either with or without leverage. You can use it, but there's no need to.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by grayfox »

Ranger wrote: Most of the people use leverage in wrong way or over levered which gives leverage bad name.

It is better to lever low volatility asset and combine with negatively correlated asset. It usually has better sharpe ratio.
Ranger is right. Most peopled leverage up a stock portfolio which is stupid.

MPT says that you hold the portfolio with the highest Sharpe slope, which is the Tangency portfolio TP, and leverage or dilute with risk-free asset. Usually TP is mostly bonds.

So for the example above, I calculated the weights for TP, maximum Sharpe slope. See below. [Note: I did this by trial and error. I used to use Excel which had a great nonlinear Solver. Now I have OpenOffice Calc and Solver is only for linear. :( ]

Code: Select all

	11.1/88.9
a	0.111
b=1-a	0.889

mu.Z	     0.05555

a^2*sigma2.X	0.000493
+ b^2*sigma2.Y	0.001976
+ 2ab*sigma.XY	0.000000
= Sigma2.Z	0.00247

Sigma.Z	0.04969	
	
Sharpe Slope	1.1180339
TP has weights 0.111/0.889 and has the highest Sharpe slope = 1.1180339.
If you are able to borrow at the risk-free rate, and lever it up 1.171:1, Z has the same expected return as the 90/10 but much lower standard deviation.

Code: Select all

             11.1/88.9   90/10
Leverage	     1.71  	1.00
Expected Ret	0.0950	0.0950
SD	             0.0850	 0.1801
Graphically, this is just moving out along the Capital Allocation Line CAL from the Tangency Portfolio TP, ramping up volatility and return. CAL is always above and to the left of the efficient frontier EF

Image

Yay, Leverage! :sharebeer
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

Rodc wrote: All those little words and yet not one numerical example. (Just saying...)
grayfox and sltultz had worked through before my post showing why leverage can have better return and sharpe ratio.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by YDNAL »

.

OK, lets make the rubber meet the road.... a challenge to ANYONE!

1. Borrow the most you can.
  • a) To stay on topic with OP's subject, take your current portfolio [say] $100K which is allocated 90/10 Total Stock/Total Bond, and borrow $100K to buy $10K Total Stock, $90K Total Bond.
    b) Make sure to document the cost of debt and repayment process.
    c) Post whatever it is that you have done in this thread.
2. We shall keep track... 2014, 3 years, 5 years, whatever period.

3. Any takers?

It's all good to theorize, hypothesize, etc. until it is time to use real money.

HERE is an interesting perspective.
Landy | Be yourself, everyone else is already taken -- Oscar Wilde
cjking
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by cjking »

Rodc wrote:Note well that grayfox's response neglected both the cost and extra risks of leverage (not just market type risk but things like call risk).

The specifics of precisely how you obtain the leverage will be needed in order to assess these factors. It would be very unusual for the final expected return and risk of a levered portfolio to beat an unleveraged one, though in some cases you might be able to do so.

There are good reasons why advice to use leverage is so rare.
I was going to raise similar issues yesterday, before I got distracted. I have several times looked at using leverage in the way suggested and come to the conclusion that though it sounds nice on paper, in reality the risks and costs make it not viable. Cheap enough leverage that can't be called and is extensive enough to cover any market eventuality isn't available to me.

The following bit from Nisi is the best summary in this is thread of what is wrong with this idea.
nisiprius wrote: In real life, if you and I have the same standard-deviation "risk," and you have a higher return, and your portfolio has leverage but mine doesn't, then we will have the same standard-deviation "risk," but you will have a higher chance of ruin, higher "black swan" risk, higher fragility.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by jackpistachio »

Hmm... so now just to figure out the Tangency Portfolio of the future, and the covariance of the asset classes over time as well! Obviously these are unknowable. We can figure out where they have been in the past, and see how they move all over the place. And then there are the events that fall well outside what one would usually expect by considering things like standard deviation.

I can give a testimonial on Landy's challenge. Did that. Failed. However, I'm not going to do 1.c) as it would be anecdotal anyway. A tough personal lesson to learn on leverage, but thankfully I learned it before I had any considerable sums to ruin myself with.
We're all nuts, but Pistachios are my favorite.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

YDNAL wrote:.


3. Any takers?

HERE is an interesting perspective.
I would, but i said this in another thread.

http://www.bogleheads.org/forum/viewtop ... 0#p1800552

"In trading, traders can play only when expected returns are positive. For eg, lever up when CAPE below 12 and reduce leverage when CAPE is above 25. "

What would winner of your competition get?

Petrocelli routinely beats from his Active fund picking strategy. Does it mean everybody should follow his strategy?
http://www.bogleheads.org/forum/viewtop ... 0&t=119028

Every investor should follow his investment strategy based on their risk tolerence level, not because of some bogus competition.

Love the bullishness of bogleheads at the market high. I have been long enough in this forum to witness despair of "stay the course no matter of valuation" strategy in the depths of recession. Also i have read ( may be in 2001 or 2002) most active thread in M* Vanguard Diehards forum "How i made my millions using moving average" :D

Also when ever "leverage" comes in this forum, Markettimer thread is pointed at. Even bogleheads are not different from general public, comparing strategy with the outcome. First of all it is single data point and next is he was under capitalized. If he struck with the strategy today and would have beaten single factor model of bogleheads handily then., every body would have told him it was just luck.
Last edited by Ranger on Sun Nov 24, 2013 10:29 am, edited 1 time in total.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by YDNAL »

Ranger wrote:
YDNAL wrote:3. Any takers?

HERE is an interesting perspective.
I would, but i said this in another thread.

http://www.bogleheads.org/forum/viewtop ... 0#p1800552
Are you saying that you use leverage, but said something else in the link? In the Queen's language, and without circular innuendo, what exactly does your post in the link say?
Ranger wrote:As others have said, it is poor analogy.

Poker has a negative expected return after rake. Also one needs to be in the game always to reach that expected return.

In trading, traders can play only when expected returns are positive. For eg, lever up when CAPE below 12 and reduce leverage when CAPE is above 25.
larryswedroe wrote:Jfet
You ONLY know that know, at the time it was not obvious to anyone that we would get out of the problem. All it would have taken were some errors in policy responses and another Great Depression might have occurred. In fact there were many like Roubini who were calling for it and Gross and El Erian were predicting years if not decades of lousy returns.
Hindsight 20/20 and it causes people to believe that even the unlikely was certain.
Best wishes
Larry
Hindsight may be 20/20, but expected return were certainly higher during that time. Why should anyone listen to market gurus, when odds are favoring traders. Traders were handsomely paid to take that risk during that time too (80% vol).

Some of the good poker players, who understands market structure have done well in the markets (David Einhorn comes to mind).
Landy | Be yourself, everyone else is already taken -- Oscar Wilde
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Ranger
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

Pardon my english, I am not an native speaker.

That said, it means what i said in the quote. Lever up, when there is opportunity and now is not the time.
YDNAL wrote:/
Are you saying that you use leverage
[/quote]

Yes.
http://www.bogleheads.org/forum/viewtop ... 2#p1687785
grayfox
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by grayfox »

YDNAL wrote:.

OK, lets make the rubber meet the road.... a challenge to ANYONE!

1. Borrow the most you can.
  • a) To stay on topic with OP's subject, take your current portfolio [say] $100K which is allocated 90/10 Total Stock/Total Bond, and borrow $100K to buy $10K Total Stock, $90K Total Bond.
    b) Make sure to document the cost of debt and repayment process.
    c) Post whatever it is that you have done in this thread.
2. We shall keep track... 2014, 3 years, 5 years, whatever period.

3. Any takers?

It's all good to theorize, hypothesize, etc. until it is time to use real money.

HERE is an interesting perspective.
I'll take the challenge. Let's say for 5 years.

However I need to be able to borrow $100K at the risk free rate which is currently 0%. Since you are proposing the challenge, are you willing to lend contestants $100K at 0 percent?

I'll put the $100K + $100K = $200K into 10/90 TSM/TBM. At the end of 5 years I'll liquidate it and repay the $100K loan, keeping the rest of the proceeds. If the remaining is less than $100K, loss. If more than $100K, profit. This would be a worthwhile experiment, purely for edification.
Last edited by grayfox on Sun Nov 24, 2013 11:16 am, edited 1 time in total.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

grayfox wrote: However I need to be able to borrow $100K at the risk free rate which is currently 0%. Since you are proposing the challenge, are you willing to lend contestants $100K at 0 percent?
It is possible. Futures have implied borrowing rate of around 0.5% now, but those contracts are big.

Assume you buy one mini SP500 contract. That contract is worth $90,000. O/N margin in that account is around $5,000. Suppose you keep $10,000 so that it will satisfy maintenance issues and keep rest in Barclay money market account earning 1%. So you are paying 0.5% for $90,000, earning 0% for $10,000 and earning 1% for $80,000.

But the problem with those big contracts, it is not possible to rebalance. However if the account is in millions it is possible with that strategy.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by market timer »

Ranger wrote:But the problem with those big contracts, it is not possible to rebalance. However if the account is in millions it is possible with that strategy.
You can use futures and fine tune using options and/or ETFs.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by market timer »

G-Money wrote:Leverage is borrowing. Investing in bonds is lending. So, really, one offsets the other.
Borrowing is likely to be short term (less than 3 months, rolled periodically), while bond investing would be 5-30 years in duration. The two do not offset. You have things like term premium, optionality, and credit risk to consider.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

market timer wrote: You can use futures and fine tune using options and/or ETFs.
I use ES future options, SPX and SPY options to maintain the delta exposure I want.

100,000 silly competition can be limiting for combination of future, option and ETF account. Portfolio margining needs more than $100,000.

I also mentioned to disprove other point mentioned in the thread, that individuals can't get low borrowing rate to offset gains because of leverage. Individual traders can get close to zero( in this case positive carry) interest rate.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by grayfox »

I ran the analysis for VFINX / VBMFX using monthly Yahoo data from Dec-1990 to Nov-2013.
From Daily Treasury Yield Curve Rates, 3-month T-Bills are yielding 0.07% which is close to zero

[1] "Mean Annual Returns & Volatilities"
VFINX VBMFX
[1,] 0.09382 0.06090
[2,] 0.14856 0.03655

VFINX had higher return than VBMFX, 9.38% vs. 6.09%, but greater volatility, 14.856% vs. 3.655%

[1] "Correlation Matrix"
VFINX VBMFX
VFINX 1.00000 0.06877
VBMFX 0.06877 1.00000

Correlation is slightly positive, 0.06877, but close to zero.

[1] "Sharpe Ratios"
VFINX VBMFX
0.1809 0.4755

:arrow: VBMFX had higher Sharpe slope, thanks to much lower volatility. Bonds usually have higher Sharpe slope than stocks because stocks are maybe 4x as volatile for 2x the return. That's the key why it is better to leverage up a portfolio with mostly bonds than to hold 100% stocks. :idea: That was the idea of the OP and it is a worthwhile theoretical result to understand.

Find Tangency Portfolio TP, weights and monthly continuously-compounded return and volatility

Portfolio weights:
VFINX VBMFX
0.073 0.927
Portfolio expected return: 0.005276
Portfolio standard deviation: 0.01047

Tangency Portfolio weights are 7.3% VFINX and 92.7% VBMFX. That's the combination to leverage up by borrowing at the risk-free rate rf = 0.07%
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by LH »

Re: A levered 50/50 portfolio is better than a 90/10 one?
No, its not.

With leverage, you can get a margin call, and blow up.

Doesnt matter if your are LTCM with some nobels or not.

In physics, you assume a frictionless environment..... there is basically no such thing in day to day experienced reality.

Econ, ditto. There is a big difference between theory and reality.

In academia, when theory disagrees with reality, oftentimes its felt reality is whats wrong. The "maths" work, screw it, we are still right. Go figure.

but yeah, risk free, frictionless, conflation of things that can work with large groups with things that work for an individual (matching over 30 years), and most of all "guaranteed", like a guaranteed private company "guaranteed" annuity for thirty years, why, if a private company takes the risk (instead of you), the risk all just goes "poof" and goes away in aggregate, because when markets tank, and bonds dont perform for years, well the money comes from.... er.... well its comes I tell ya. Because its "guaranteed" .... Its all great stuff.... in theory.

So do the math, lever up (read market timer thread first) and give us a blow by blow on how it goes if you choose to do it, its interesting, if tragic, reading expectantly.

but no, don't do it in reality.

Heh, grayfox is giving me 20 year (not very lucid) flashbacks. LIke to see that stuff again here, gives me a mild headache. "RobertH"? and gummy used to go that stuff some. Kudos.

LH
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Rodc »

Tangency Portfolio weights are 7.3% VFINX and 92.7% VBMFX. That's the combination to leverage up by borrowing at the risk-free rate rf = 0.07%
You have nailed THE tangency portfolio to three significant digits. Impressive indeed! :)

Now that we know the future so precisely the way forward is clear.

I do wish you and ranger luck and good fortune even if my path is different.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by LH »

Rodc wrote:
Tangency Portfolio weights are 7.3% VFINX and 92.7% VBMFX. That's the combination to leverage up by borrowing at the risk-free rate rf = 0.07%
You have nailed THE tangency portfolio to three significant digits. Impressive indeed! :)

Now that we know the future so precisely the way forward is clear.

I do wish you luck and good fortune even if my path is different.


ditto good luck : )
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by telemark »

Standard deviation is not risk, only a fairly imperfect way of measuring risk, and one of the reasons for the imperfection is that risk is not fungible. There are different kinds of risk and they behave in different ways. Perhaps I've missed something, but I don't see where MPT attempts to model this. As others have already said, leveraging introduces call risk, which tends to show up when you can least afford it.
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Ranger »

Rodc wrote:
I do wish you and ranger luck and good fortune even if my path is different.
Thanks wish you the same.

To be clear, I am leveraged player since 2001-2002 but not vanilla leverage described in this thread or market timer thread. I am mostly long/short momentum commodities/currencies/Asset classes along with short volatility on indices (sorry Taleb) and some spreads.

I have done extremely well during those years (still yearning for 2008-2009 type of vol).


There was lot of negativity when market timer thread too, when he started writing about leverage and options.

I am done here and g/l all.

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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by YDNAL »

Ranger wrote:Pardon my english, I am not an native speaker.
Ranger wrote:100,000 silly competition can be limiting for combination of future, option and ETF account. Portfolio margining needs more than $100,000.
OK. Since you are not a native speaker, perhaps you don't understand that the challenge is to proactively show what you are doing, so that everyone has the benefit to measure its results.... peer review, if you will.

It is NOT necessarily a "silly $100,000" and it can be a *silly $1 million* and you borrow another $1 million.
Ranger wrote:I have done extremely well during those years (still yearning for 2008-2009 type of vol).
So, you have $1M and can borrow $1M... can't you?
YDNAL wrote:.

OK, lets make the rubber meet the road.... a challenge to ANYONE!

1. Borrow the most you can.
  • a) To stay on topic with OP's subject, take your current portfolio [say] $100K which is allocated 90/10 Total Stock/Total Bond, and borrow $100K to buy $10K Total Stock, $90K Total Bond.
    b) Make sure to document the cost of debt and repayment process.
    c) Post whatever it is that you have done in this thread.
2. We shall keep track... 2014, 3 years, 5 years, whatever period.
Perhaps I've wasted my time because you don't do "vanilla leveraging" and you are more sophisticated - just as someone like Ed Quian.

grayfox, no free lunch.
1. The portfolio is 50/50 TSM/TBM - defined in the OP - and I suggest 2x leverage.
2. The cost to you is 1.4% - same as 5-year Treasury - and the loan is callable.
Landy | Be yourself, everyone else is already taken -- Oscar Wilde
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Akiva »

stemikger wrote:This is what Warren Buffett says about leverage:
If you’re smart, you don’t need leverage. If you’re dumb, you have no business using it.
Which is really ironic given how much leverage he uses...
grayfox wrote:Now if you can't borrow at the risk-free rate, don't blame me. Bring it up with Bill Sharpe. It's called Modern Portfolio Theory.
You can get really close by using futures or deep in the money options. Those are probably substantially better than a margin account unless you are with IB and have a huge account.

Re: the original question, just pull the monthly return data for S&P futures and bond futures and do your weighting there. Those have the cost of leverage built in.

FWIW, Schwager reported some years ago that the risk parity approach (what you are talking about) had the highest sharpe ratio with 30/70 and needed about 10-20% leverage (i.e. very little) to put it back at the same risk as a more aggressive stock portfolio (but with higher returns).
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Dxbinvestor »

I posted this in some other thread but using simple math seems the 50/50 is better, and you don't have much call risk.. People always give slippery slope sky is falling leverage examples but say you lever 1.5:1 on something like LQD, you never get a margin call even at lowest point of 2008, and your positive carry is 200-300 bps using simple IB portfolio margin. If you want to be more aggressive, you could lever JNK at same rate and your yield on cash goes up to ~9%, and again, no margin call even at record low. Sane leverage seems fine to me..

Please post an example where sane bond fund leverage would get called / forced to sell?
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by lostInFinance »

nisiprius wrote:The right conclusion to draw from this is not that miracles are possible, and not that you can win against a casino, but that infinite lines of credit don't exist.
If you're considered too big to fail and can borrow from the Fed and the Fed can print money, is that considered very close to an infinite line of credit? I just need to figure out how to get on the "too big to fail" list...
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Re: A levered 50/50 portfolio is better than a 90/10 one?

Post by Akiva »

Some people in this thread are saying the same incorrect things I responded to here. As for whether this is a good idea, it's hard to say. Bonds have had a very good run, so the benefits of this strategy are likely inflated if you just look at historic data. Furthermore, getting cost-effective leverage is harder for a retail investor, but not impossible. See the linked post for more information.
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