In the 1950s, Professor Harry Markowitz of the City University of New York developed an ingenious approach to investment that has become known as modern portfolio theory (MPT). Unlike traditional asset management, which focuses on predicting individual stock price movements using fundamental or technical analysis, his system looks at the performance of a portfolio of assets based on the combination of its components' risk and return. His hypothesis and subsequent work were so revolutionary that Markowitz was a joint Nobel Laureate for economics in 1990.

The system Markowitz developed, however, had to wait until the late 1970s to be put to practical use. The task of applying modern portfolio theory was made possible only with the advent of computers that could handle the vast number of calculations and range of historical data needed by the model. Thus, portfolio management today melds theory and technology to optimize portfolio performance.

### The magic of diversification

To most investors, the logic of diversification is intuitively obvious: "Don't put all your eggs in one basket." Diversification helps spread risk between countries, currencies and markets. It enables us to benefit from opportunities as they arise around the world. It provides us with a means of hedging our bets against crises (such as war or oil shortages) and unexpected events (stock market crashes or natural disasters). Diversification reduces risk. Modern portfolio analysis has shown that even a random mix of investments is less risky than putting all your money in a single stock. In other words -- and this is not always obvious -- for the same amount of risk, diversification can increase returns.
The technical underpinnings of MPT are complex, drawn from financial economics and probability and statistical theory. But a simple answer to the question of why diversification reduces risk can be stated in the following way:

Imagine that a portfolio contains two risky assets: one that pays off if the sun shines, another that pays off if it doesn't/ A portfolio that contains both assets will always pay - rain or shine. Adding one risky asset to another can reduce the overall risk of our all-weather portfolio. The crucial insight of MPT is this: the risk of an individual asset is of little importance to the investor; what matters is its contribution to the portfolio's risk as a whole. This is the magic of diversification.

### Asset returns: a matter of probability

Since we are speaking here of risky assets, we cannot be sure about the return on these assets. Not 100% at any rate. But by using the past to project into the future, investors can determine the likelihood of a certain return. The expected return on a risky asset is based on the probabilities attached to all possible rates of return for the asset. With a 50-50 chance of a sunny day, the expected return on our all-weather portfolio with one asset returning 210% and the other 10% is its weighted average: 15%.
In many problems involving probabilities -- in portfolio theory as well as in actuarial calculations and opinion polling, to name just a few applications -- the probabilities of all possible outcomes are assumed to have a bell-shaped normal distribution. The point in the middle of the curve is the stock's expected one-year return of 7%. The probability of the return being less than 7% is 50% as is the probability of it being more. The area under the normal curve is the probability of realizing a return between the extreme points on the curve. This probability is equal to 1.

The historical annual volatility or the degree of variation from the expected return is measured by the standard deviation. For Stock XYZ, let's say this has been 15%. Assuming a normal distribution, we can say with 68.26% certainty that the actual one-year return will be somewhere between a low of -8% and a high of (15+7)%=22% (the expected return of 7% minus one standard deviation of 15% and 7% plus 15%). Similarly there is a 95.46% probability that the actual return will be between -23% and 37% (or within a range of two standard deviations). Notice that the actual return of a less volatile stock, say, one with a standard deviation of 7% will move within a narrower range of possible returns. For a stock with an expected return of 7%, the range is between -7% and 21% with 95.46% probability.

### Trading off risk and return

Diversification involves a trade off between risk and return. If you were certain what the weather would be like tomorrow, then you would buy only that asset yielding the maximum return under those conditions, and no trade off would be necessary.
MPT makes some very reasonable assumptions about the way investors behave regarding risk. Although some investors can take more risk than others, investors are assumed to be risk- averse. A risk-averse person is one who when faced with assets which promise to provide the same return will choose the asset with the lowest risk. In order for investors to accept higher risk, they will want to be compensated with the potential for earning a higher return and vice-versa.

Studies in the United States have shown that small-company stocks are some of the most profitable, albeit riskiest, investments you can make. Between 1926 and 1994, these have returned more than 12% annually compared to some 10% for large- company stocks, 5% for long-term government bonds and 4% for Treasury bills. The standard deviations (volatility) were around 35%, 20%, 9% and 3%, respectively.

### How does diversification reduce risk?

The mechanism to reduce risk is the way returns on assets move together. If, using our all-weather example, both assets were to pay off 20% on a sunny day and nothing on a cloudy day, then returns on these two assets are said to be perfectly correlated (correlation coefficient = 1) and there would be no point in diversifying. These asset prices would rise and fall in unison, so owning both assets would be superfluous. The trick is to find assets that are less than perfectly correlated, or even negatively correlated.
For this reason international diversification makes very good sense. Numerous studies have documented the benefits of going global with your investments. These have shown that including foreign securities in a portfolio can increase returns for a given level of risk. The efficient frontier of a portfolio constructed with only domestic stocks.

The chart shows that investing in different industries within a single country is riskier than investing in just one industry across different countries. A globally diversified portfolio represents less risk than a diversified domestic portfolio. The key is the smaller correlation between domestic securities and foreign ones than between different domestic securities. Country-wide factors such as stability, business conditions, monetary and fiscal policies, and demographics tend to have the most impact on domestic securities, so financial markets from one country to another will tend to differ significantly. If you have shied away from investing abroad, you have actually been subjecting your portfolio to greater risk.

It is also interesting to note that risk falls steeply as you begin to diversify. With a holding of around 40 stocks, all the benefits from diversification have been almost nearly achieved. Like anything else, diversification has its limits. And as world markets become more integrated, the limits will be more easily reached.

Investors should still be able to profit handsomely from diversifying. Although markets are not completely independent -- all correlations on returns are positive -- many correlation coefficients are still significantly below one. U.S. equity markets are more closely correlated with the markets of Canada (0.81) and the U.K. (0.63) than with Japan (0.44) or Germany (0.41). One good combination of stocks to own would be from Switzerland, Japan, U.K. and Australia.

Emerging markets also vary in the degree they move with trends in the world's major economies. For example, Hong Kong and Argentina, with their currencies pegged to the dollar are vulnerable to rises in U.S. interest rates, as is Singapore, with a high dollar component in its trade-weighted currency basket.

### Rewards for taking risks -- if you're in it for the long haul!

Risk is almost inevitable in any investment. Most assets carry the uncertainty of whether they will realize a return in the future, and if so, how much. Stock prices move up and down and dividend yields may vary from year to year. Perhaps the only risk-free way to keep your money is to lock it up in a fire-proof safe. Unfortunately, if you wait long enough, it loses in purchasing power. Even securities issued with the full faith and credit of the U.S. government are not riskless. The price of a U.S. Treasury bond maturing in 30 years may fall in a year if interest rates rise.
Our concepts of risk and uncertainty naturally impose negative biases to investments with high volatility. Yet research in different countries on the historical performance of stocks -- considered the most volatile asset class -- show that investors are rewarded for taking on greater risk if they have the discipline to hold on to their investments. A buy-and-hold strategy can smooth out the bumps in the stock markets.

During the period between 1926 and 1994, the best one-year return in the U.S. stock market was a 54% rise in 1933 and the worst was a 43% decline in 1931. Over a holding period of 10 years, the best annualized return was a positive 20% and the worst was a negative 1%. If we increase the time frame to 20 years -- any 20 years between 1926 and 1994 -- investors are always assured of a positive return ranging between 17% and 3%.

Similarly, if you look at the development of German common stocks in the past 120 years, the worst fall was a loss of 38%. But in Germany, it seems investors don't need as much patience as in the U.S.: a holding period of 10 years returns an average of 35% in the best 10-year case and positive 1% in the worst case. For a time frame of 15 years, the stock market's volatility moderates to a range of 24% and 4%.

In order to increase portfolio returns, investors have to take on greater risk. Injecting stocks into a portfolio for higher returns therefore translates to a bumper ride. To smooth out the bumps, investors would do well to (a) diversify globally and (b) hold a portfolio of stocks for long enough periods. You may not win a Nobel Prize, but you will be on the right road to investment success.

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Jurg M. Lattmann is a Swiss investment counsellor and expert in
Swiss annuities.
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*Copyright © 1996 by Jurg M. Lattmann.
More information on international investment can be found at
The Offshore Entrepreneur.