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Friday, April 07, 2006


Stock Risks - Relative and Absolute

There are several measures of risks. Many outfits create their own proprietary measures of risks to confuse things further. Here is an explanation that is simple and moderately technical.

Relative risk, also called market risk, of a stock or stock fund with respect to an appropriate broad index is called BETA. For example, if a US stock fund changes by 4% when SP500 Index changes by 5%, then the fund BETA is “approximately” 0.8 (= 4/5). By definition, index BETA is 1.0. Choice of an appropriate index is important. While SP500 Index is appropriate for US stocks and stock funds, EAFE Index is appropriate for international stocks and stock funds. While BETAs for international stocks can be computed against SP500 Index, such BETAs are less useful and must be interpreted carefully; correlation factor is useful in such interpretations but that would be the subject of another mote technical posting.

Precise determination of BETA involves comparison of, say, monthly percent changes in a stock fund with those in the index over, say, a three-year period. Then using simple statistical analysis (linear regression), BETA and ALPHA are determined to satisfy the following relationship:

(% monthly change in stock fund) = BETA x (% monthly change in index) + ALPHA

ALPHA is taken as an indication of fund management’s savvy because it represents return over or under what can be expected based upon BETA alone.

ALPHA = (% monthly change in stock fund) - BETA x (% monthly change in index)

Positive ALPHAs are supposed to be good, while negative ALPHAs are supposed to be bad. Well, that is the theory. In practice, BETAs tend to persist over time and do contain useful information. But ALPHAs tend to fluctuate a lot and are less useful. Also, most aggressive stock funds have negative ALPHAs while many conservative balanced funds with 40% or less stocks have positive ALPHAs. This does not mean that all conservative balanced funds are better managed than all aggressive growth funds. So, comparing ALPHAs works only within a peer group.

If the market went down 30% and your fund with BETA of 0.8 went down 24%, should you be happy? Yes and no. Yes, because your fund delivered the expected performance – no more and no less. But that will hurt because 24% loss is a big hit in an absolute terms for most of us. How to control this absolute risk? That is through standard deviation (STD_DEV or SIGMA). It is a measure of how much, say, monthly returns deviate from the average monthly return over, say, a three-year period. No distinction is made among positive and negative deviations, and no benchmark index is involved in its determination. Under ideal conditions – that never exist in practice – prices will be contained between AVG (+/- ) STD_DEV for 68.26% of the time, or for simplicity, two-thirds of the time. Prices will be contained between AVG (+/- ) 2 STD_DEV for 95.44% of the time – this is the rationale for Bollinger Bands in that once the price moves out of 2 STD_DEV band around moving AVG, the fund is way overpriced or underpriced, although the time frame is for daily pricing over a few days only (20 days in Yahoo Finance). Standard Deviation also tends to persist over time but it does fluctuate. For SP500, standard deviation is typically in 15-20% range (annualized) although in some three-year time frames, it can be around 10% (annualized) only. Standard Deviations can be determined for any asset class: stocks, bonds, TIPS, REITs, money market instruments. Because its determination is independent of any benchmark index, standard deviations can be compared across different asset classes. They are the highest for sector funds and negligible for money market instruments.

You can therefore control absolute risk through standard deviations. If the general stock market standard deviation is 18% (annualized), and general bond market standard deviation od 4%, a conservative investor can mix stocks, bonds and money market instruments to have a portfolio standard deviation of 8-10% (annualized); this is achievable with 50-50 stock-bond mix. An extremely conservative investor may limit portfolio standard deviation in 6-8% range (annualized); this is achievable with 20-80 stock-bond mix. Intermediate bonds are best for portfolio construction. Long term bonds are bets upon interest rate changes and do not have a good risk/reward in general. Junk bonds have standard deviations comparable to equities so they really belong in stock category, not in bond category.

If you are super aggressive, then you can have sector funds that have standard deviations of 2-3 times of the general equity market (i.e., STD_DEV of 40-60% annualized), or you can use leverage (margin) to increase standard deviation of an otherwise normal portfolio. One approach employed by hedge funds is to construct a low risk “sure fire” strategy and then use large amounts of leverage (e.g., 4:1 debt:equity). But in reality, there is nothing that is “sure fire,” and hedge fund performances are all over the board. Many hedge funds have just collapse spectacularly because things went the other way to their supposed "sure fire" way. And some times people can get too greedy, and put too much weight on the advice of Noble Laureates or capability of quants – remember LCTM that had 40:1 debt:equity that was made possible by extreme secrecy?

Serious investing is all about controlling risks, and not about maximizing profits. If you manage risk to your comfort level, you would be well rewarded for staying the course. Within your level of risk, you can adjust the portfolio mix, change the nature of stocks and bonds that you hold, and trade moderately, so this is not a buy and hold approach.

Where do you get some of this information at low or no cost? From Yahoo Finance, AAII, and Morningstar. There are many subscription-based services that will also provide this type of data.


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