My daughter is a millionaire

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When viewed in the context of your statements, it seems logical that the way to achieve this would be to take the optimal non-leveraged portfolio and essentially leverage everything equally to achieve the desired level of risk.

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only if the cost of leverage is equal across assets, which I'd bet it isn't.

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I had always listened to the standard advice of don't invest on margin and pretty much just took it at face value, but now that I understand things better, I feel like using leverage may not be as irresponsible as many (well-meaning) folks seem to think. It will just require a good understanding of my true portfolio risk levels and my risk tolerance.

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the "standard advice" is standard because most people don't really have that understanding.

[DcifrThs]

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Here is my take on it. It seems to me that the primary goal of diversification should be to find uncorrelated or negatively correlated assets in order to reduce portfolio volatility, NOT to simply mix in lower volatility assets to reduce portfolio volatility. The problem is that these assets have different risk/return characteristics. My understanding of the strategy you've been discussing is that it helps to approximately equalize risk between asset classes by using leverage with the lower risk assets (which also results in similar returns between asset classes), so that you can effectively manage the portfolio based more on the correlation between assets and less on the risk profiles of the particular assets. The result should be a portfolio with roughly the same returns as a 100% stock portfolio (or whatever you are using as the "benchmark" risk), but with lower volatility due to the lack of correlation between the assets. Similarly, it seems that you could design a portfolio with similar risk to 100% stocks using these ideas, and obtain a higher expected return. Obviously, if those two sentences are correct, you could also find a middle ground with less risk and more return than stocks. Do I have the basics concepts right? I'm particularly curious as to whether my statement about how to "correctly" diversify is correct. Thanks!

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This is the same way I interpret Barron's opinion, and demonstrates a good understanding of diversification benefits. The hard part, then, is determining the correct "benchmark" risk. If you're benchmark risk is equal to or above all the volatilities of your individual assets, you'll be levering things up to maximize return. If its lower, though, you'll wind up "levering down" by making, say, your 40% US equity allocation actually 30% US equities and 10% risk-free bonds. In reality, this would be accomplished by repo-ing less bonds for those assets you do have to lever up rather than taking both long and short risk-free bets that wind up offsetting. At some point, the "benchmark" variance will be such that the optimal portfolio using this method has net zero leverage, (that is to say, the long and short risk-free assets used to lever other allocations up or down cancel each other out and are not needed at all), which should give the same result as a standard portfolio optimization model that doesn't consider leverage.

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repo'ing things isn't the only way to get leverage. you really only have to repo TIPS (or find that leveraged fund) since there is no other real way to do it for inflation linked bonds.

for nominal bonds, you can use futures.

if you want to lever down (for equities, private eqeuity, and commodities), you aren't allocating the money to the same bonds. you're allocating it to a constant maturity 3 month tbill.

lets say your goal is to have an equally weighted portfolio of:

20% global equities
20% global TIPS
20% global aggregate bonds (nominal bonds + corporate bonds)
20% private equity
10% real estate
10% commodities

further, you want each of those exposures geared to have a 5% total risk level.

instead of a straight 20% equity exposure (assume 15% volatility), you would have about 6.67% invested in equities and 13.33% invested in 3 month tbills.

instead of just 20% in TIPS (about 4% volatility), you'd take your 20% allocation, repo it and invest 25% of it in more tips, and the rest in 3 month tbills.

instead of just your 20% global bond allocation (about 8% volatility), you'd hold 12.5% in that exposure and 7.5% in 3 month tbills.

instead of your 20% private equity exposure via funds assuming they exist (and about a 12% volatility..but this is very much open for debate), you'd hold 8.33% of that allocation in PE and 11.77% in 3month tbills.

instead of your 10% real estate allocation (about 12% vol), you'd do the same in REITs as for PE except cut in 1/2.

finally, for commodities (about 20% vol) you'd put 5% in the commodity fund or whatever and the rest in 3 month tbills.

so you see, CASH (3month tbills) has become a significant (if not majority) holding and your "net leverage" is nowhere near 1 (a zero levered portfolio is levered 1:1). instead (i haven't added it all up) it is closer to like 0.5:1 (meaning it is delevered substantially...about half). i don't see a case where your leverage is net'd out to one, but if it exists that just means holding more or less Tbills. you'll never be repo'ing the bonds you hold in cash though. you'e be repo'ing the bonds to which you want to increase your exposure (note you're also never NOT repo'ing some bonds to reduce their leverage).

thus your portfolio will look like something i'll paste later on today in a pie chart since this is a good exercise for me anyways.

now that you know how to calculate the deleverage, i'll give an example of total leverage... to lets say a 30% volatility (which would be pretty sick with about a shape ratio of maybe .55)

equities: use futures, which are cheap to gain leverage with less cash

bonds: again, you can use futures as they exist and are liquid and cheap

private equity: here you'd have to actually borrow money somehow to gain the extra exposure since i don't think futures/forwards swaps etc. are available.

TIPS: this is tough since you lose inflation protection via repos (you only get 1 inflation protected coupon payment since you're borrowing at the new mkt rate basically each time) you have to use a mix of repo & physicals.

Real estate: here there are REIT futures so you can gain leverage that way

commodities: same thing, use futures.

so here, the total leverage would be like 3:1 instead of 0.5:1 and you'd be experiencing some major swings.

the SIMPLEST thing to do would be ot just target the 15% (or ~12% if global) vol of equities. that would gain you extra return on a well diversified portfolio. your sharpe ratio would jump from about 0.3-0.4 to about 0.55-0.65. i think the max you could ever obtain would be 0.65 or so.

note again though that you are never repo'ing the same bonds you are "not repo'ing" and having things net out. you are using whatever means you have at your disposal to gain leverage (be it by buying on margin from a broker if you can re: PE, or using Repo's). i think this is the part on which you were getting stuck.

hope this helps.
Barron

[DcifrThs]

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When viewed in the context of your statements, it seems logical that the way to achieve this would be to take the optimal non-leveraged portfolio and essentially leverage everything equally to achieve the desired level of risk.

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only if the cost of leverage is equal across assets, which I'd bet it isn't.

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I had always listened to the standard advice of don't invest on margin and pretty much just took it at face value, but now that I understand things better, I feel like using leverage may not be as irresponsible as many (well-meaning) folks seem to think. It will just require a good understanding of my true portfolio risk levels and my risk tolerance.

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the "standard advice" is standard because most people don't really have that understanding.

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the cost of leverage overall is very minimal in comparison to the "savings" you get in return. the variability of cost of leverage accross assets means that you just have to either suck it up and take that drift down from the "optimal" portfolio or re-shuffle your allocations to take the cost into account.

Barron

[DcifrThs]

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Here is my take on it. It seems to me that the primary goal of diversification should be to find uncorrelated or negatively correlated assets in order to reduce portfolio volatility, NOT to simply mix in lower volatility assets to reduce portfolio volatility. The problem is that these assets have different risk/return characteristics. My understanding of the strategy you've been discussing is that it helps to approximately equalize risk between asset classes by using leverage with the lower risk assets (which also results in similar returns between asset classes), so that you can effectively manage the portfolio based more on the correlation between assets and less on the risk profiles of the particular assets. The result should be a portfolio with roughly the same returns as a 100% stock portfolio (or whatever you are using as the "benchmark" risk), but with lower volatility due to the lack of correlation between the assets. Similarly, it seems that you could design a portfolio with similar risk to 100% stocks using these ideas, and obtain a higher expected return. Obviously, if those two sentences are correct, you could also find a middle ground with less risk and more return than stocks. Do I have the basics concepts right? I'm particularly curious as to whether my statement about how to "correctly" diversify is correct. Thanks!

[/ QUOTE ]

This is the same way I interpret Barron's opinion, and demonstrates a good understanding of diversification benefits. The hard part, then, is determining the correct "benchmark" risk. If you're benchmark risk is equal to or above all the volatilities of your individual assets, you'll be levering things up to maximize return. If its lower, though, you'll wind up "levering down" by making, say, your 40% US equity allocation actually 30% US equities and 10% risk-free bonds. In reality, this would be accomplished by repo-ing less bonds for those assets you do have to lever up rather than taking both long and short risk-free bets that wind up offsetting. At some point, the "benchmark" variance will be such that the optimal portfolio using this method has net zero leverage, (that is to say, the long and short risk-free assets used to lever other allocations up or down cancel each other out and are not needed at all), which should give the same result as a standard portfolio optimization model that doesn't consider leverage.

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I hadn't considered that, but it makes sense. Still, for someone like me who is only 23 years old and currently willing to accept the risk inherent in the the S&P500, for example (meaning I wouldn't be too risk averse to put everything in an S&P500 index fund), it seems that I could put these ideas to work to achieve an S&P-beating return with the same volatility. When viewed in the context of your statements, it seems logical that the way to achieve this would be to take the optimal non-leveraged portfolio and essentially leverage everything equally to achieve the desired level of risk. I had always listened to the standard advice of don't invest on margin and pretty much just took it at face value, but now that I understand things better, I feel like using leverage may not be as irresponsible as many (well-meaning) folks seem to think. It will just require a good understanding of my true portfolio risk levels and my risk tolerance. Also, I find it interesting that it is possible to lever an entire portfolio at least to a small degree by repoing bonds (and possibly other assets?) rather than using the traditional margin account. If I'm understanding what I've been reading, the repo rate is quite a bit less than the rates charged to borrow in a normal margin account. Obviously borrowing at above the risk-free rate will decrease your risk-adjusted performance since you are taking on additional risk in order to achieve proportionally less additional gains (due to the cost - above the risk free rate - of borrowing money). Repo rates that are approximately equal to the risk free rate don't create this negative impact.

I am still not clear on how to weight everything based on how the various assets correlate, but that doesn't really seem to be the topic of discussion, so I'll save that for another thread. Besides, I don't really know enough about that to ask any intelligent questions right now.

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i went through an example above...but that gives you weightings. i can try to do one w/ correlations taken into account later.

repos are not the only way to leverage and you have to OWN the bonds first to do that.

some things do require normal type borrowing or margin type account which drives up that borrowing cost.

this gets even more complicated when you realize that each month you *should* determine where you stand and rebalance your portfolio to get back to your initial allocations.

hope this helps.
Barron

[Nomad84]

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The SIMPLEST thing to do would be ot just target the 15% (or ~12% if global) vol of equities. that would gain you extra return on a well diversified portfolio. your sharpe ratio would jump from about 0.3-0.4 to about 0.55-0.65. i think the max you could ever obtain would be 0.65 or so.

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Thank you so much for sharing your knowledge with us. I can't believe how much I'm learning from this discussion. If I understand you correctly, this quote is basically saying that if these techniques are applied correctly, it is possible to (almost) double the excess returns of a 100% equity portfolio at the same risk level. I could live with that [img]/images/graemlins/cool.gif[/img]