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Monday, August 15, 2011

Determining an Appropriate Asset Allocation for your Portfolio

"Investors have too often extrapolated from recent experience. In the 1950s, who but the most rampant optimist would have dreamt that over the next fifty years the real return on equities would be 9% per year? Yet this is what happened in the U.S. stock market. The optimists triumphed. However, as Don Marquis observed, an optimist is someone who never had much experience." - Triumph of the Optimists:  101 Years of Global Investment Returns

Deciding upon an asset allocation strategy for one's portfolio is not as simple as relying on the hackneyed "stocks for the long-run."  Based on the long-term data in Triumph of the Optimists, it is generally true for most countries that stocks outperform bonds and bonds outperform bills [see Table 4-1].  The higher return earned by stocks is compensation for the additional risk taken on.  From Table 4-3 and 4-2, the minimum annual real return [real return is the nominal return minus inflation] for stocks during 1900-2000 for the 16 countries listed was negative 48%, the maximum annual return was 90%, the standard deviation averaged about 23, which measures how widely returns will vary around the average, and the average return was 7.6%.

If the returns in this sample follow a normal distribution (which they don't by the way - see Nassim Taleb's The Black Swan), then 68% of the time stocks will return between (15.4)% and 30.6% and 95% of the time stocks will return between (38.4)% and 53.6%.  The same exercise can be done for bonds and bills noting the average annual real return falls to 1.69% and 0.57% and the standard deviation falls to 12 and 8, respectively.  The standard deviation is sometimes mistaken as a measure of risk, but it is generally much better to think of risk in terms of a permanent loss of capital.  I like to think of standard deviation as the number of nights a year one will spend thinking about a given investment instead of sleeping.  While stocks may provide a higher average return over a given period of time, the dispersion of returns is much wider than that of bonds and bills.  Bonds and bills provide a much more predictive return for part of the portfolio, although at the cost of higher potential returns.

One of the great, free resources on the Internet for building a portfolio is Paul Merriman's "Fine Tuning Your Asset Allocation."  First the caveat, the data is historical, which means the table showing the hypothetical returns of balanced asset class portfolios (1970-2010) will not be predictive of future returns.  The returns also assume a 1% management fee is deducted annually with the exception of the S&P 500 column.  If one wanted to, one could use the asset class forecast data from GMO, LLC to estimate future 7-year returns to update the estimated returns.  For a 40% equity and 60% bond mix, the estimated 7-year return as of July 31, 2011 would be approximately 4% annualized compared with 9.4% in the chart.  The difference is due primarily to the over-valuation of bonds and to a lesser extent stocks compared with the 1970-2010 period.  With that being said, it does provide a great way to assess one's tolerance for volatility and to choose a broad asset allocation that makes sense with one's investment time horizon.

Take for example, a 40% equity and 60% bond mix.  The worst 60 month period provided a 1.6% annualized return.  As equity exposure increases beyond that point, the annualized returns become negative over the worst 60 month period.  This point of negative returns may be different if we were to look forward into the future, but in general, assuming one purchased intermediate term individual bonds, the higher the bond allocation, the less likely one would be to lose money (in nominal terms, i.e. not adjusted for the effects of inflation) over a 60 month period.

There are also interesting trade-offs when accepting more equity exposure.  If we calculate a simplistic Sharpe Ratio for the portfolios, it continually falls as the equity exposure increases.  In essence, the dispersion of returns the investor is facing grows with increased equity exposure and return potential.  This is shown in the worst month, worst 12 month, and worst 60 month data.   Lubos Pastor provides interesting thoughts on why the notion that stocks are less volatile over long periods of time than in the short-run may be overstated due to the uncertainty facing an investor looking out over a long and uncertain future as opposed to academics looking in the rear view mirror.  Most individuals can determine quite quickly where their comfort level lies, or more importantly, what makes sense given their investing horizon.  Then adjusting the data to look forward provides a more realistic expectation of future returns.  Unfortunately, the worst month, 12 months, and 60 months going forward is impossible to predict.  The search for higher returns often comes with more sleepless nights.

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