Thursday, May 18, 2006

Understanding Risk

Even if you are not mathematically inclined, bare with the geektalk on this post for what I hope will be a useful revelation

My monthly newsletter from T Rowe Price included a note from one of their bond fund managers who noted that a 50-50 stock and bond allocation has been shown to produce 85% of the returns of stock-only portfolios while substantially reducing volatility. I flipped the page - I'm not the kind of guy who sells when the market crashes, and hence don't worry about volatility.

But maybe I should. A new day brings new insight, and I wondered what volatility does to "terminal values", which really is what you and I care about. A terminal value is the value of an investment after some lengthy period of time. So, for example, how does volatility affect the value of a $1,000 investment after 20 years? Intuitively, we all seem to think it doesn't matter - as long as the timeframe is "sufficiently long", the returns will approximate the mean returns, things will average out. But is that true?

So as I chomped on my lunch, I wrote a little program to simulate terminal values (yes, sad is the life of a geek!) And the results were revealing. I simulated two artificial portfolios - fund A has a mean return of 8% and standard deviation of 8%, while fund B has a mean return of 16% and a standard deviation of 24%. The simulated mean returns after 20 years, not surprisingly showed that fund B was a lot better than fund A - your $1,000 investment was now worth $20,540 in the former, as opposed to $4,690 in the latter. Ah, the joys of compounding!

But what about the ranges? Your terminal values in fund A could have ranged from $1,700 to $11,600, while in fund B, you could have been left with $630 to $178,440. That is, even after what you consider a long time, the volatily in fund B could have caused you to lose money, although it just might have made you phenomenally rich!

This is the part left out of the literature for the common investor. Risk matters ... in fact, risk is pivotal. I understand that many publications are trying to get excessively conservative investors to embrace risk (the ones who refuse anything riskier than a bank deposit), but the average Joe and Jane do have to worry about risk. This is especially true when they read stories of people who invested in a speculative issue or hot real estate market and ended richer than you could ever dream - yes, it can happen to you, but you could lose your shirt and a lot more.

It strikes me that a statistically appropriate measure while planning for retirement would then be to study this dispersion, and have a certain degree of confidence in achieving some basic milestone. (So you may want to be 90% confident of retiring with a $1 million)

Postscript Since the time of this post, I have noticed several articles and mutual fund companies refer to similar probabilities, even though they are closer to a 75-80% chance of adequate savings (a higher probability causes a dramatic rise in the required savings, as one can determine from the shape of a Bell curve). Nevertheless, I still think this aspect is underplayed in articles and most personal investors do not have an appreciation for risk.

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