Modeling the Optimal Portfolio
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Modeling Multiple Asset Classes
You might have noticed that TIP$TER doesn't break your portfolio down into multiple equity asset classes, each with its own expected return, standard deviation, and multiple cross-correlation coefficients with other asset classes.
That's because (1) it is way too complicated for the average user and (2) TIP$TER can model any diversified portfolio you want, provided that it resembles the behavior of one of TIP$TER's many distribution models or the S&P 500's complex, serially correlated pattern of volatility.
Modeling A Small-Value Tilted Portfolio
Assume that you have a well-diversified, but small-value tilted portfolio. Presumably, you expect your portfolio to generate a higher return than a cap-weighted total stock market portfolio. When calculating your expected risk premium, add in the incremental size and/or value return premiums you expect for your portfolio. Pages 14 and 15 of the Credit Suisse Global Investment Returns Yearbook 2009* illustrates how you might go about estimating a size or value premium.
But it would be prudent to be modest in your estimated premiums. After all, the secret of small and value is out, and most financial planners recommend a small-value tilted portfolio. The size and value premiums, going forward, are likely to be less generous than in the past.
Also, if you are modeling a small-value tilted portfolio, you should probably increase the expected volatility. After all, a small-value tilted portfolio will likely be more volatile than a pure cap-weighted total stock market portfolio.
If you want to model your small-value tiltled portfolio with an exploratory simulation of a standard-deviation-adjusted S&P 500 dataset, you can do that too – with a little Advanced User trick.
Advanced User TIP$TER Trick
By default, TIP$TER's mean-adjusted historical data set has the same volatility as the original data set (i.e., 19.7% standard deviation for rolling annual returns from Jan. 1871-Dec. 2011). However, TIP$TER can scale its set of historical S&P 500 return data to have a volatility (standard deviation) equal to the user-specified volatility.
To keep the interface simple for most users, TIP$TER mostly conceals the "annualized standard deviation of returns" input behind a "Reserved" comment when the "exploratory simulation" option is selected.
Sophisticated users who wish to adjust the volatility of the historical return data set, however, can still access the standard deviation input spinners (by zooming on this section of the spreadsheet or by unprotecting the spreadsheet and closing or moving the comment).
Modeling a Mean-Variance Optimized Portfolio
You might have noticed that TIP$TER does not include a mean-variance optimizer (MVO). Again, it doesn't need to.
There are numerous mean-variance optimizers (MVOs) out there, each capable of back-testing data to identify an optimal historical portfolio with a given mean and standard deviation.
Have you identified an optimal historical portfolio? Are you confident that history will repeat itself and that the historical returns and correlations that will either make or break your optimal portfolio will persist?
TIP$TER's creator is skeptical of those assumptions. So are other respected authorities. William Bernstein, in his "Mean Variance Optimization: The Thinking Man's Ouija Board" article, calls MVOs "a recipe for disaster."
But TIP$TER the program is agnostic. TIP$TER can model your mean-variance optimized portfolio.
What annualized real return and standard deviation do you expect from that optimal portfolio? Either make your own estimates, or use your favorite mean-variance optimizer to produce those values.
Calculate the difference between the expected annualized real return on your optimized portfolio and the real yield on TIPS. Then plug that number into the "Extra expected return on stocks" input.
Next, choose a Monte Carlo simulation model:
Now, enter the expected standard deviation from your optimized portfolio.
Then run the simulation. It's as simple as that.
*Credit Suisse is a trademark of Credit Suisse Group Société, with which Prospercuity claims no association, connection, affiliation, or sponsorship.
Prospercuity also claims no association, connection, affiliation, or sponsorship with William Bernstein.