Risk Latte - You have math in your Portfolio!

You have math in your Portfolio!

Rahul Bhattacharya
Jun 17, 2006


If there was no formal concept of volatility, like a sigma or standard deviation, correlation and mean, in our working lives, would we ever think of diversifying our wealth into stocks, bonds and currencies? Without a formula for portfolio volatility or variance and correlation, which fund manager would talk about diversification? Without the portfolio math and matrix algebra which analyst would talk about "sector correlation", "principal factors" and all that stuff?

Have you ever thought why you think of portfolio diversification? You think of it, because there is something called Capital Asset Pricing Model (CAPM), something called volatility and correlation, something called variance-covariance matrix, something called mean-variance analysis. You think about diversification because there is math in it.

Did you know that John Maynard Keynes, the famous twentieth century economist, and a successful investor of his own money, deeply distrusted the notion of diversification? We came across a couple of passages from his writing on a website*. Here it is (from J M Keynes):

".........One's knowledge and experience are definitely limited and there are seldom more than two or three enterprises at any given time in which I personally feel myself entitled to put full confidence. "

" A small gamble in a large number of different companies where I have no information to reach a good judgment, as compared with a substantial stake in a company where one's information is adequate, strikes me as a travesty of investment policy. "

Actually, such was the mainstream thinking until the mid-1960s. The emphasis was on the opposite of diversification; to know the companies well, to understand the operations and to look for only a handful of companies with operations that can be understood clearly and with solid earnings and dividends.

But Harry Markowitz and Alexander Sharpe overturned that thinking in the mid-1960s. They gave us the mean-variance analysis and the formula for portfolio volatility. They gave us the CAPM. They put math in our portfolios. Financial information and knowledge got subsumed in mathematical constructs and models.

We know very well that volatility isn't just standard deviation or a number from Black-Scholes calculator it is the sum total of all the information that we don't have. From time to time we also wonder that maybe it is only Warren Buffet, or a handful of others like him who has ever come to understand this business of investment. But we have to admit that even we have no choice but to make a living out of the math in finance.


* We came across this passage in a website www.quanthome.com.

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