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Historical risk/return of two-fund Vanguard portfolios
Old 03-16-2010, 12:26 PM   #1
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Historical risk/return of two-fund Vanguard portfolios

More Geeky stuff, long.
Sorry .

The main idea of "modern portfolio theory" seems to be that a combination of uncorrelated assets can produce a portfolio with lower volatility than any of the member assets.

It is not hard to put together some two-fund portfolios to see how this has worked out, so I did.

I wrote a script that creates 11 portfolios of two funds. The percentage asset allocations range from 0/100 to 100/0 in steps of 10. The script calculates and plots the risk/return of each portfolio. The risk is represented by the daily percentage change in NAV; the return is represented by the equivalent APR.

The time period can vary for each plot because for each pair I use the longest period for which data is available for both funds.

Since the crash, we are in a topsey-turvey world. Suddenly, some historically lower-risk, lower-return assets such as bonds are yielding higher than historically higher-risk stocks over reasonably long periods. Risk/return plots look upside-down.

These are just some examples of what the risk/return results have been. I do not mean to imply that these portfolios are in any way better than any others. I haven't tried to use this approach to select optimum portfolios (yet).

Stock/Bond portfolios
For example, here is the risk/return for portfolios of various allocations of Total Stock Market and Total Bond Market.
Total stock and Total Bond.gif
The highest yield occurs at 0% stocks! Even so, adding 10% stock reduces the volatility of the portfolio a little (while also reducing the return). Adding more stock has been a losing strategy. It just increases the volatility and reduces the return.

Bond/Bond portfolios
I was surprised to see that even Bond/Bond portfolios displayed the same effects. Here are the results for portfolios of Int. Term Tax-Exempt and Short Term Inv. Grade. However, note that the axes are different and the amount of risk reduction is actually very small. The highest return is 0% Int. Term Tax-Exempt.
Int. Term Tax-Exemp and Short Term Inv. Grade .gif

Stock/Stock portfolios
Stock/stock portfolios also show similar behavior. Here are portfolios of Total International Stock and Total Stock Market. The highest return is 0% Total International.
Total International Index and Total Stock Index.gif

Portfolios containing balanced funds

I was also surprised to see that adding the high volatility fund such as High-Yield Corporate to a low volatility fund such as Wellesley can actually reduce the volatility of a well-balanced fund such as Wellesley. It also reduces the return. The highest return is still for 100% Wellesley.
High-Yield Corporate - Wellesley Income.gif

Barbell portfolios
Sometimes combining low-risk bonds with high-risk stocks does not produce lower volatility than the less risky asset. Here, no portfolio of Short-Term Treasury and Small-Cap Growth has lower volatility than the treasuries alone. However, the highest yield is for 100% Small-Cap Growth.
Short-Term Treasury and Small-Cap Growth Index.gif

I don't have anything profound to say about any of this. I just thought it interesting.

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Old 03-16-2010, 02:12 PM   #2
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It seems that it is hard to make real valid conclusion on these charts, because most of the are periods are fairly short starting in the mid 90s.

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Old 03-16-2010, 09:23 PM   #3
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It does show that the best returns are always had by chosing just the one option that has the best return. Providing you know which one that is!

So this is all an exercise in reducing standard deviation without compromising too much on return. Ideally we'd be able to select the best return/risk point and then leverage/dilute as needed to reach our acceptable risk level.
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