are 10 unique asset classes, then an equal allocation only risks one-tenth of the portfolio. The more groups, the less the risk.

Diversification is accomplished by appljing as many of the following techniques as possible-

1 . Selecting individual maikets from different groups. Trjing to trade those products with as little interrelationship (low covariance or correlation, discussed in Chapter 3, "Regression") as possible. Traditionally fiitures markets have been categorized into sectors of interest rates, currencies, index, grains, livestode metals (indusfrial and precious), foods, and miscellaneous. The last group accounts for fibers, woods, oil. and other products with little relationship to other maikets.

There is a laiger category called financials. -,A-hich encompasses interest rates, currencies, and index maikets While these sectors tend to move on their own most dsjs, they are known to have very sjmpathetic, correlated readions to unexpected economic news. This overriding similarity must he considered when allocating assets within a portfolio.

Even without the close economic ties shown by the financials. there is considerable interadion between all of these groups. Without special news, agricultural maikets have little to do with metals and each moves according to their own fiinds

mentals; however, a radical change in the value of the U.S. dollar or interest rates could move all prices in the same diredion. For example, rising interest rates are bad for commodities that must be stored, because it increases those costs. In rum, investors will sell gold and farmers will sell soybeans rather than pay a laiger carrying charge.

Slow changes in the value of the U.S. dollar will affed export maikets: changes in interest rates will directly impad the stock index. A crisis in the potato maiket. however, has little effed on other areas of the economy When selecting those markets to be used in a diversified portfolio, it is necessary to check the historical similarity of equity pattems as well as consider the major forces that currently drive the market-both historic and predictive sides of the problem. When properly seleded. diversification will reduce ride as shown in Figure 23-6.

2. Multiple sjStems. Using more than one sjstem will reduce risk, provided the sjstems are not similar. Techniques may appear different and yet be highly correlated. A mog average sjstem, ARIMA model, and point-and-figure are very different methods, but all are trend-following. If the sensitivity of all three systems is similar (as determined by the number of trades per year), the equity pattems U-il] also be similar. For sjstem diversification, it is best to select sfrategies with different functional attributes. For example, the following list gives sjstems that are likely to be less correlated and techniques within each method that tend to be different.

a. Trend-following (moving averages or point-and-figure) b. Countertrend (stochastic or contrary opinion) c. Spreading (interdelivery, intercommodity, arbifrage, product) d. Fundamental

All four techniques are very different. Fundamentals may be frending in nature but should have a longer time perspective. The four ty es of spreads all offer excelp

lent diversification.

3. Balanced rid;. Equalizing risk is necessary if the seledion of different commodities and sjdems is to offer proper diversification. Traditionally, price volatility or market value is used to equate risk; however, this method tends to concentrate frading in those products that are lead active-and less likely to be profitable. For example, in early 1986, com was trading at $3 per bushel and the S&P 500 Index at 200. making their confrad values $15,000 and $100,000, respectively. Equalizing confrad

FIGURE 23-6 Effect of diversification on rid;.

Number ot market* (different futures categones)

values would mean trading seven com to one S&P even though the likelihood of profiting in com is far less than that of the S&P

Equalizing rid; must account for the way the trading model pertbrms in the selected martlets; most sjstems do best in volatile periods. Because the most profitable strategies require some substantial price move, thej concentrate on martlets that have greater volatility Therefore, it is both easier and better to diversify by dishibuting the investment among different sjstems and evaluating only the correlations in equity A djnamic cspital allocation will be necessarj as one sjstem becomes successful and its contribution to both profits and risk becomes disproportionately laige. Withdrawing trading cspital from the more successful sjstems at such times will maintain equal rid; among sjdems and stabilize equity pattems.

These three justifications for diversification have their negative side as well. Diversfication can mean lower profits. If there are equal retums from trading all maikets and all sjstems, the diversified retums reduce risk and leave profits at the same high level. However, this never hsppens. It is not likely that silver and soybeans will be profitable at the same rate, nor is it to be expected that two sjdems will parallel themselves in performance using two distinctly different techniques.

A classic example is the use of a sjstem that actually loses money but has such a negatively correlated performance to one with a high retum that the results of using them together are obviously better than either of them alone (Figure 23-7). Because sjdem retums only a small loss, it does litUe to affect the profitability of Sydem A. It will, however, sharply reduce the equity drops by being profitable during periods when Sjstem A is losing.

Portfolio Calculations

Deciding which sjstems and maikets should be traded at the same time, in an effort to reduce rid; through diversification, is an entire field of expertise called portfolio management. While maikets have alwajs changed reflecting economic policy and the grow-th of participation, more recent years of globalization have made portfolio management much more difficult. As more inatitutions trade intemational markets as they do their own, they cause a higher correlation of price movements throughout the world. This increase in correlation between previously unrelated areas makes it more difficult to reduce rid; through diversification, and makes previous asset allocations obsolete. One answer to this problem is simply to rebalance the portfolios more often, regrouping assets by their similar price movements.

FIGURE 23-7 Stabilizing equity using negatively correlated sjstems.

Traditionally, the analjst builds up a portfolio fran the expectations of the individual items to be traded. Even more sophisticated portfolios are constructed by selecting marfcets from groups that have been chosen, in advance, after performing a correlation analjsis. Those that show different performance pattems qualify as potential assets in the portfolio. Once selected, the expected retum of the portfolio is the weighted average of the expected retums on the individual components of the portfolio," assuming each component is invested with the same percentage of the total.

= Yw,E(R,y

- tv„E(R„)

The worth of a portfolio is not only its retum, but its risfc; therefore, the variance of the portfolio becomes a important criterion in deciding which combination of assets create the best results:

where erf is (he variance of the renjms of marker i, and Cj is the covariance berween the returns of msu-ket i arid the returns of market /. The covariance, C, between two markets is

Given two portfolios with the same retums, the one with the smaller variance is more desirable; when the variances are the same, the portfolio with the highest retum is best. For a portfolio of only two assets, the calculations needed for expected retum and variance are.

E{R) = WxEiRi) + Mzf(R2)

It is important to compare portfolios using this basic comparison of retum and ride however, it is not the entire picture. When evaluating the relationship between a large number of data points, there may be only one case in which an exfreme price movement would have caused a fatal loss of equity. That one case can be lost in the statistics, because the large number of normal cases overwhelm one exfreme. For ety, it is necessary to also loofc at the maximum portfolio loss. In addition, we must assume that the largest historic loss will be exceeded sometime in the future, if only by chance (consider the number of heads or tails in a row based only on the number of coin flips). Ideally, we should try to imagine the worst-case scenario, in which globalization increases the correlations, and the past events are not fully representative of future events.

Spreadsheet Approach