Monday, February 21, 2011

3 easy steps to getting rich

Now that I'm almost finished with my MBA, I know everything. Among my newfound knowledge is a deep understanding of securities markets. So when people ask me how they should invest their money, I'm thrilled to help.

Not one to sit on my laurels, I encourage people to come up with their own active portfolio, and then combine it with a common, well-diversified index, such as the S&P 500. "How do I create an active portfolio?" you ask. It's pretty easy. Just find a few stocks that look good -- spend a few weeks doing in-depth valuations, or throw darts; the odds of success are the same -- and estimate alpha for each one. Then you need to figure out how much of your money to put into each stock. Use this formula:

wi0 = [ai/si2(e)]/[Sai/si2(e)]

No problems so far. You're just taking each alpha, which is a nonmarket premium specific to each security, and dividing it by the idiosyncratic variance of those returns, as a fraction of the sum of these ratios across all your stocks! Now that you have these weights, you need to decide how much you want to invest in this active portfolio, vs. the passive index. Again, this is a breeze -- just plug and chug!

wA = [aA/sA2(e)]/[E(rm - rf)/[s2(m) + (1 - bA)(aA/sA2(e))]
... where bA = Swibi
... and aA = Swiai
... and sA2(e) = Swi2si2(ei)

All you'll need to know here are the alphas and betas of your active portfolio, which are simply weighted sums of the individual alphas and betas (beta, of course is the covariance of a security with the market, divided by the market variance), as well as the active portfolio's idiosyncratic variance, which is a sum of the product of the square of each security's weight and each security's firm-specific variance, which itself is the square of the standard deviation. Oh, and you'll need to know the expected market premium, which is the difference between market returns and the risk-free rate; you can use historical data to calculate this if you want. Oh, and the market variance -- again, this can be researched on your own. And that's it! You'll know what percent of your money to invest in this active portfolio, which, thanks to your innate overconfidence (which you might want to compensate for with an overconfidence factor), you think is better than the market portfolio everyone else is using, and you can just subtract that weight from 1 to determine how much to invest in the passive index.

Now you're almost done! Finally, you'll want to assess your natural level of risk aversion to figure out the most comfortable mix for you between this new-and-improved risky portfolio and a risk-free asset, such as Treasury Bills. Mine is 1.8. You should be able to assess yours, if you don't know it already, through various psychological surveys. You can feel free to use mine for the time being; I'll need it back, though. Anyway, take that number and plug it into this formula:

w* = [E(rp) - rf]/Asp2

This will tell you how much to put in this mixture of the active and passive risky portfolios, and how much (the remainder) to stick into T-bills. And you're done! Good luck to you.

And to me. I have an Investment Management midterm this morning.

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