Risk, Return, and Portfolio Allocation

MEASURING RISK AND RETURN Risk and return are the building blocks of finance and portfolio management. Once the risk, expected return, and correlations between asset classes are specified, modern financial theory can help investors allocate their portfolios. The last chapter 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 investors will see that uncertain inflation will make their portfolio allocations depend crucially on their planning horizon.

RISK and HOLDING PERIOD

. There is a far more rapid decline in the difference between the best and the worst returns for equities than for the fixed income securities as the holding period increases. Stocks are riskier than bonds and t-bills over 1 or 2 years but in every 5 years only 11.9% of the stocks have been worse that the worst performance of bonds and bills. In 10 years the worst performance of stocks was better than that of bonds and bills, while in 20 years stocks have never fallen below inflation, although bonds and bills have fallen 3% inflation. In 30 years the worst stock performance fell 2.6% above inflation. It is riskier to purchase bonds than stocks in the long run

Holding Period Stocks Outperform Time Period Stocks Outperform Bonds Treasury Bills 1 Year 1802-2012 1871-2012 58.8 61.3 62.1 66.9 2 Year 60.5 64.1 62.9 70.4 3Year 67.2 68.7 70.2 73.3 5Year 67.6 69.0 68.6 74.6 10 Year 72.3 78.2 83.8 20 Year 83.9 95.8 87.5 99.3 30 Year 91.2 100.0 Percentage of Time Stocks Outperform Bonds and Bills over Various Holding Periods

. As the holding period increases the profitability that stocks will outperform fixed-income assets increase dramatically. For 10 year horizons stocks beat bonds by nearly 80%, for 20 years it was about 90% of the time and for 30 year horizons it was almost 100% of the time.

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 this figures.

Although the standard devvıatıon of stock returns ıs; 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 the return on a portfolio of equities falls to less than three-fourths that of bonds or bills The standard deviation of average returns falls nearly twice as fast for stocks as for fixed income assets as the holding period increases.

If asset returns follow a random walk, the standard deviation of each asset class will fall by the square root of the holding period A random walk is a process whereby future returns are completely independent of past returns

The dashed bars in Figure show the decline in risk predicted under the random walk assumption.

But the historical data show that the random walk hypothesis cannot be But the historical data show that the random walk hypothesis cannot be maintained for equities. This occurs since the actual risk of average stock returns declines far faster than predicted by the random walk hypothesis because of the mean reversion of equity returns. The standard deviation of average returns for fixed-income assets, on the other hand, does not fall as fast as the random walk theory predicts. This is a manifestation of mean aversion of bond returns.

Mean aversion of bond returns is especially characteristic of Mean aversion of bond returns is especially characteristic of hyperinflations, where price changes proceed at an accelerating pace, rendering paper assets worthless. But mean aversion is also present in the more moderate inflations that have impacted the developed economies. Once inflation begins to accelerate, the inflationary process becomes cumulative, and bondholders have virtually no chance of making up losses in their purchasing power.

Correlation between stock and bond returns

The correlation coefficient ranges between –1 and +1 The correlation coefficient ranges between –1 and +1 and measures the comovement between an asset’s return and the return of the rest of the portfolio. Figure will show us the correlation coefficient between annual stock and bond returns from 1926 to 2012.

Why stocks are less risky than bonds in the long run? Its to minimize risk. The longer they are held for the better. People are becoming more conservative. Investor purchasing power of their wealth.

EFFICIENT FRONTIER

The efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Modern portfolio analysis and is the foundation of asset allocation models. Created by Harry Markowitz in 1952 Aims to balance securities with the greatest potential returns with an acceptable degree of risk 1990 Nobel Prize in Economics for his work on the efficient frontier and other contributions to modern portfolio theory

Expected Return %

Conclusion Stocks are definitely riskier than fixed assets but in the long run we see that they are safer for the investor Despite the drastic changes in inflation no one knows the exact value of the dollar in the near future. Only purchasing power of diversified portfolio can be told hence its better to buy a treasury bill bond of 30 years.