CHAPTER 2

RISK, RETURN AND ASSET ALLOCATİONWhy Stocks Are Less Risky than Bonds

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MEASURING RISK AND RETURN Risk and return are the building blocks of finance and portfolio

management.Once the risk and expected return of each asset are specified, modern financial theory can help investors determine the best portfolios.

But the risk and return on stocks and bonds are not physical constants.

Despite the overwhelming quantity of historical data, one can never be certain that the underlying factors that generate asset prices have remained unchanged.

One must start by analyzing the past in order to understand the future.You can remember the first presentation is prepared by friends showed that not only have fixed-income returns lagged substantially behind those on equities but, because of the uncertainty of inflation, bonds can be quite risky for long-term investors.

In this chapter one shall see that because of the changing nature of risk over time, portfolio allocations depend crucially on the investor’s planning horizon

RISK AND HOLDİNG PERİOD

For many investors, the most meaningful way to describe risk is by portraying a “worst-case scenario.” The best and worst after-inflation returns for stocks, bonds, and bills from 1802 over holding periods ranging from 1 to 30 years are displayed in Figure 2-1.

Maximum and Minimum Real Holding Period Returns, 1802 through December 2006

Note that the height of the bars, which measures the difference between best and worst returns, declines far more rapidly for equities than for fixed-income securities as the holding period increases.

Stocks are unquestionably riskier than bonds or Treasury bills over one- and two-year periods. However, in every five-year period since 1802, the worst performance in stocks, at –11 percent per year, has been only slightly worse than the worst performance in bonds or bills.

And for 10-year holding periods, the worst stock performance has actually been better than that for bonds or bills.

For 20-year holding periods, stock returns have never fallen below inflation, while returns for bonds and bills once fell as much as 3 percent per year below the inflation rate for two decades. This wiped out almost one-half the purchasing power of a bond portfolio

For 30-year periods,the worst returns for stocks remained comfortably ahead of inflation by 2.6 percent per year, a return that is not far from the average return on fixed-income assets.

INVESTOR RETURNS FROM MARKET PEAKS

Many investors, although convinced of the long-term superiority of equity, believe that they should not invest in stocks when stock prices appear high. But this is not true for the long-term investor. The after-inflation total return over 10-, 20-, and 30-year holding periods after the eight major stock market peaks of the last century is shown in Figure 2-2.

Average Total Real Returns after Major Twentieth-Century Market Peaks ($100 Initial Investment).

Even from major stock market peaks, the wealth accumulated in stocks is more than four times that in bonds and more than five times that in Treasury bills if the holding period is 30 years.

If the holding period is 20 years, stock accumulations beat those in bonds by about twoto-one.

Even 10 years after market peaks, stocks still have an advantageover fixed-income assets. Unless investors believe there is a high probability that they will need to liquidate their savings over the next 5 to 10 years to maintain their living standard, history has shown that there is no compelling reason for long-term investors to abandon stocks no matter how high the market may seem.

if investors can identify peaks and troughs in the market,they can outperform the buy-and-hold strategy.

STANDARD MEASURES OF RISK

The risk—defined as the standard deviation of average real annual returns— for stocks, bonds, and bills based on the historical sample of over 200 years is displayed in Figure 2-3. Standard deviation is the measure of risk used in portfolio theory and asset allocation models.

Risk for Average Real Return over Various Holding Periods, 1802 through December 2006 (Historical Risk versus Risk Based on Random Walk Hypothesis)

Although the standard deviation of stock returns is higher than for bond returns over short-term holding periods, once the holding period increases to between 15 and 20 years, stocks become less risky than bonds. Over 30-year periods, the standard deviation of a portfolio of equities falls to less than three-fourths that of bonds or bills. The standard deviation of average stock returns falls nearly twice as fast as for fixedincome assets as the holding period increases.

Theoretically the standard deviation of average annual returns is inversely proportional to the holding period if asset returns follow a random walk. A random walk is a process whereby future returns are considered completely independent of past returns. The dashed bars in Figure 2-3 show the decline in risk predicted under the random walk assumption.

VARYING CORRELATION BETWEEN STOCK AND BOND RETURNS Even though the returns on bonds fall short of that on stocks, bonds

may still serve to diversify a portfolio and lower overall risk. This will be true if bond and stock returns are negatively correlated, which means that bond yields and stock prices move in opposite directions. The diversifying strength of an asset is measured by the correlation coefficient. The correlation coefficient, which theoretically ranges between –1 and +1, measures the correlation between an asset’s return and the return of the rest of the portfolio. The lower the correlation coefficient, the better the asset serves as a portfolio diversifier. Assets with negative correlations are particularly good diversifiers. As the correlation coefficient between the asset and portfolio returns increases, the diversifying quality of the asset declines.

The correlation coefficient between annual stock and bond returns for six subperiods between 1926 and 2006 is shown in Figure 2-4.

Correlation Coefficient between Monthly Stock and Bond Returns

From 1926 through 1965 the correlation was only slightly positive, indicating that bonds were fairly good diversifiers for stocks.

From 1966 through 1989 the correlation coefficient jumped to +0.34, and from 1990 through 1997 the correlation increased further to +0.55.

This means that the diversifying quality of bonds diminished markedly from 1926 to 1997.

EFFICIENT FRONTIERS

Modern portfolio theory describes how investors may alter the risk and return of a portfolio by changing the mix between assets. Figure 2-5, based on the 200-year history of stock and bond returns, displays the risks and returns that result from varying the proportion of stocks and bonds in a portfolio over various holding periods ranging from 1 to 30 years.

Risk-Return Trade-Offs for Various Holding Periods, 1802 through December 2006

The square at the bottom of each curve represents the risk and return of an all-bond portfolio, while the cross at the top of the curve represents the risk and return of an all-stock portfolio. The circle falling somewhere on the curve indicates the minimum risk achievable by combining stocks and bonds. The curve that connects these points represents the risk and return of all blends of portfolios from 100 percent bonds to 100 percent stocks. This curve, called the efficient frontier, is the heart of modern portfolio analysis and is the foundation of asset allocation models.

Investors can achieve any combination of risk and return along the curve by changing the proportion of stocks and bonds. Moving up the curve means increasing the proportion in stocks and correspondingly reducing the proportion in bonds. As stocks are added to the all-bond portfolio, expected returns increase and risk decreases, a very desirable combination for investors. But after the minimum risk point is reached,increasing stocks will increase the return of the portfolio but only with extra risk.

RECOMMENDED PORTFOLIO ALLOCATIONS

Portfolio Allocation: Percentage of Portfolio Recommended in Stocks Based on All Historical Data

What percentage of an investor’s portfolio should be invested in stocks?

The answer can be seen in Table 2-2, which is based on standard portfolio models incorporating both the risk tolerance and the holding period of the investor.7 Four classes of investors are analyzed: the ultraconservative investor who demands maximum safety no matter the return, the conservative investor who accepts small risks to achieve extra return, the moderate-risk-taking investor, and the aggressive investor who is willing to accept substantial risks in search of extra returns.

INFLATION-INDEXED BONDS

Until the last decade, there was no U.S. government bond whose return was guaranteed against changes in the price level. But in January 1997, the U.S. Treasury issued the first government-guaranteed inflation- indexed bond. The coupons and principal repayment of this inflation-protected bond are automatically increased when the price level rises, so bondholders suffer no loss of purchasing power when they receive the coupons or final principal. Since any and all inflation is compensated, the interest rate on this bond is a real, or inflation adjusted, interest rate.

CONCLUSIONNo one denies that in the short run stocks are riskier than fixed-income assets. But in the long run, history has shown that stocks are actually less risky investments than bonds. The inflation uncertainty that is inherent the paper money standard that the United States and the rest of the world have adopted indicates that “fixed income” does not mean “fixed purchasing power.” Despite the dramatic gains in price stability seen over the past decade, there is still much uncertainty about what a dollar will be worth two or three decades from now. Historical evidence indicates that we can be more certain of the purchasing power of a diversified portfolio of common stocks 30 years in the future than the principal.

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