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Tuesday, 07/22/2003 5:32:18 AM

Tuesday, July 22, 2003 5:32:18 AM

Post# of 47097
The most important concept in investing is diversification.

Regardless of the actual strategy we use, if we don't properly diversify we open ourselves to more risk than we need to take.

The question, of course, is how do we properly diversify?

There are a number of strategies that range from completely useless to very good. I'll mention a few here.


EQUAL FUNDS
The simplest way to diversify is to decide which stocks you'd like to own and divide your investment funds equally between them. Then, periodically, you rebalance. This diversification strategy is better than nothing, but lacks any real ability to use synergies that might be present in your portfolio.


SHARPE RATIO
A better method is to use the Sharpe ratio (SR). Since you can type "sharpe ratio" into Google and read all about it, I'll refrain from giving the details here. Suffice it to say, however, that it is a measure of reward/risk. The higher the value, the better the investment (from a reward/risk perspective).

Note that a high sharpe ratio doesn't necessarily mean the highest return or the lowest risk. Rather it means that that's the best you could have done when reward and risk are taken together.

To calculate SR, for a stock, you need the stock's expected return and standard deviation. You also need the best risk-free rate (typically what they're paying for cash).

For AIMers, you need to calculate the return and standard deviation on AIM's results, not the underlying security's price.

This makes it a little more difficult to use because you have to obtain your AIM results and then use them to calculate expected return and standard deviation. If you use the underlying security price directly, it won't work correctly for AIM.

Okay, so we can calculate the SR. Great! Now what?

As it turns out, once we have the SR for all of our stocks, we can use a simple method to diversify more intelligently than just throwing equal amounts of cash at our stocks.

Here's what we can do...

1) Compute the SR for each stock in our portfolio.

2) Sum all of the SR values (I'll call this the srSUM).

3) Divide each stock's SR by srSUM. This gives the percentage allocation for that stock.

For example, let's say I have 3 stocks in my portfolio (A,B and C). Let's further say that I've calculated the SR for each stock as follows:

A has an SR of 2.5
B has an SR of 1.5
C has an SR of 4.0

In this case srSUM is 8 (i.e. 2.5 + 1.5 + 4.0).

I then divide the SR for stock A by the srSUM of 8 to get 2.5/8 = 0.3125

If I do the same for B and C, I get 0.1875 and 0.5 respectively.

This means that I should invest about 31% of my money in stock A, about 19% in stock B and about 50% in stock C.

The advantage of this strategy is that the better reward/risk stocks get a larger share of our investment funds (which is a far more logical way to go than the simple equal allocation strategy I described above).

However this strategy doesn't take into account the possible interactions between securities in a portfolio. But these interactions can be significant (for example, adding a risky stock to a less-risky portfolio can actually cause the entire portfolio's risk to decrease).


MODERN PORTFOLIO THEORY
A strategy that does take interaction into account is Modern Portfolio Theory (MPT). This strategy seeks to provide portfolios, consisting of various weightings of stocks, that maximize returns for a given risk or minimize risk for a given return.

Calculating these portfolios require you to have the Mean and standard deviation for a stock as well as a covariance matrix (which is just a table that lists how stocks behave relative to one another). You can also get by with correlation coefficients (which you can then use to calculate the covariance).

For those that don't like to think about these things, the reason I bring it up is to explain a very important point.

First, you have to either estimate or otherwise obtain (e.g. via historical data) these values in addition to estimating or obtaining the Mean and standard deviation values.

If you happen to be off by just little (especially for the Means), the resulting asset allocation can be significantly changed. It's hard enough to obtain a reasonable Mean, but adding covariance values (you need one between each pair of stocks) just increases the odds that you won't get something quite right.

Once you have these values you can feed them into an algorithm, called a Mean-Variance optimizer (or you can use some other algorithm that does almost the same thing), that will calculate your optimal portfolios.

You can then select a portfolio based on either the maximum risk you're willing to assume or the minimum return you're willing to accept. Once you've selected your portfolio, you invest your funds according to the specified allocation.


SHARPE RATIO AGAIN...
Interestingly enough, you can use the Sharpe Ratio to automatically select the best portfolio for you (from a reward/risk perspective). This frees you from worrying about what risk you're willing to assume or what minimum return you'd like. Once MPT has returned the set of efficient portfolios, you calculate the SR for each one and choose the one with the highest SR. It's easy and it's automatic. Your computer can even do it for you.

Note that, as above, you need to calculate the Mean, Standard Deviation and Covariance on your AIM results -- not the underlying security.

Unfortunately, because of the estimating inputs problem, MPT doesn't always work well in the real world. For historical data you can't beat it. However as a predictive device, it can fall short.

Having said that, however, MPT works fairly well if you can somehow feed it accurate inputs or you use index funds over long periods of time.


THAT'S ALL THERE IS TO IT
So there you have it. Three methods of diversifying your portfolio. If you're not currently diversified, you should be. Even using the "blindly allocate an equal amount of funds to a number of stocks" method is better than nothing.

However if you invest just a bit more time, you can use the work of a couple of Nobel Laureates to more intelligently diversify your portfolio. And that's got to be worth a huge sum of money somewhere down the road.







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