Momentary Diversion: Of Eggs and Baskets

After publishing my first post yesterday I realised there was a contradiction in my post. I explained that given I am paying off a mortgage on an apartment and I work in property finance that I was overweight in property and therefore excluding it as an asset class. However, I included property and banking companies in my (very) long list because “Your Industry” was recommended for inclusion in “The Motley Fool Investment Guide”.

On a related note, I also said my aim was to construct a portfolio of shares from 12 companies, but I didn’t explain how I came up with the number 12.

How are these two things related you ask? They both come under the heading of “diversification”.

Diversification is a fundamental concept in investing which doesn’t require a lot of explanation. If you put all your money in one investment and it tanks, you’ve done your dough. But if you put half in one investment and half in another, it’s less likely that both will tank at the same time, therefore investing in two investments is less risky that investing in only one.

Having said it doesn’t require a lot of explanation, there has been a lot of work done on trying to quantify the benefits. The book “Modern Portfolio Theory and Investment Analysis, 5th Edition” by Elton and Gruber includes a table measuring the effects of diversification (page 61). What they did is look at monthly price increases, ie ‘returns’ of stocks on the New York Stock Exchange. For each stock they calculated:
1. the average monthly return, ie how much in percentage terms the stock went up on average each month; and
2. the variance of the returns, ie a measure of how much the return varies from the average.

[If you don’t like maths you can ignore this paragraph and just accept that there is a way to put a figure against how much the return may differ from what you expect it to be. For the next paragraph where you see the word “variance” think “riskiness”.] If a stock goes up 1% per month on average we know that its highly unlikely it will go up exactly 1% every month. One month it might go up 0.5%, the next 2%, etc. To calculate the variance, for each month you calculate the difference between the actual return and the average return and square it (multiply the figure by itself). The reason to square the figure is to make the negatives positive, eg actual return of 0.5% less average return of 1% gives a difference of -0.5%. If you have a difference of -0.5% in one month and +0.5% in the next month, the average of the differences over two months is zero, which implies that the return each month always equals the average. By using the square of the difference each month, it removes this problem. The variance is then just the average of all the squares of the differences. (For those who like statistics, the standard deviation is the square root of the variance).

So having calculated these figures for every stock listed on the New York Stock exchange they then calculate the average variance of all the stocks. The figure was 46.619. They then calculated the average variance from investing in two stocks. It was 26.839. So, on average, by investing in two stocks instead of one, you almost half (58%) your risk. Doubling the number of stocks again to four, results in an average variance of 16.948. Note, the risk has decreased, but not by as much - the variance of holding four stocks is 63% of the variance of holding two stocks. They continued to calculate the variance of increasingly larger portfolios and (mathematically) calculated the best you can do is reduce the variance to 7.058 for a portfolio with an infinite number of securities.

So when deciding on the number of securities to hold in a portfolio, the more the better in terms of risk, but the less the better in terms of work required in maintaining the portfolio. I decided on 12 because it seemed a good trade off. A portfolio of 12 shares had an average variance of 10.354. At this point every time you add two extra shares to the portfolio you reduce the variance by less than 5%. (It remains to be seen whether I actually have the time to concentrate on this many companies.)

It should be remembered, however, that I’m assuming here that (1) shares listed on the ASX will behave in a similar way to shares listed on the New York Stock Exchange and that (2) the way share prices behaved in the past will be the way they behave in future (3) that the 12 shares I select will be sufficiently different from one another to achieve this level of risk reduction.

So that explains the 12 shares, but what to do with the banking and property shares on my long list. The above would suggest that I should cull them now, however Warren Buffet (you know it wouldn’t be long until his name came up), has other views. He believes “that a policy of portfolio concentration may well decrease risk if it raises, as it should, both the intensity with which an investor thinks about a business and the comfort level he must feel with its economic characteristics before buying into it. In stating this opinion, we define risk, using dictionary terms, as ‘the possibility of loss or injury’.” (refer “The Essays of Warren Buffett: Lessons for Investors and Managers”, compiled by Lawrence A. Cunningham, Section II.C. Debunking Standard Dogma). Basically, he is saying that the more you know about an investment the less likely you are to invest in something that will lose you money. So by concentrating on gaining greater knowledge of fewer investments you are decreasing your risk.

Extrapolating this logic, you are likely to have a greater knowledge of companies in your own industry because you live and breathe it every day. You are never going to gain, through research alone, the level of knowledge of another industry that you have of your own. On the other hand, imagine you work for ANZ, which recently announced job cuts. The closing price was $14.87 on 24 December 2008. The closing price a year earlier was $27.46, that’s a fall of 46% in one year. Imagine if you have just lost your job and your investment portfolio had fallen 46% in a year. You wouldn’t be happy. Hopefully, if you were in this situation, your knowledge of the industry and ANZ would have led you to sell the ANZ shares (and possibly look for a new job too) long before this happened. If you had sold your shares, you would then need a place to put the money, so we still get back to needing to diversify.

(Note, the Yahoo Finance site is great for looking up historical prices, look for the link under the “Research” heading on the left hand side of the page: http://au.finance.yahoo.com/investing)

Warren Buffet goes on to say “if you are a know-something investor, able to understand business economics and to find five to ten sensibly-priced companies that possess important long-term competitive advantages, conventional diversification makes no sense to you. It is apt simply to hurt your results and increase your risk.”

Twelve isn’t too much more than ten, so I will stick with it for now. I will also leave the property and banking shares in the list for now because I do want to learn more about these industries and because I am interested in seeing how they rate against everything else. Time will tell if they make final cut - back to the process in the next post.