Question

The article "Rethink Diversification to Raise Returns, Cut Risk" (San Luis Obispo Tribune, January 21,2006 ) included the following paragraph: In their research, Mulvey and Reilly compared the results of two hypothetical portfolios and used actual data from 1994 to 2004 to see what returns they would achieve. The first portfolio invested in Treasury bonds, domestic stocks, international stocks, and cash. Its 10 -year average annual return was \(9.85 \%\) and its volatility-measured as the standard deviation of annual returns-was \(9.26 \%\). When Mulvey and Reilly shifted some assets in the portfolio to include funds that invest in real estate, commodities, and options, the 10-year return rose to \(10.55 \%\) while the standard deviation fell to \(7.97 \% .\) In short, the more diversified portfolio had a slightly better return and much less risk. Explain why the standard deviation is a reasonable measure of volatility and why a smaller standard deviation means less risk.

Short answer

The standard deviation is a reasonable measure of risk or volatility because it quantifies how much returns can deviate from the average return, providing a measure of uncertainty or risk. A smaller standard deviation indicates less risk because it means there is less variation in returns, often as a result of a diversified portfolio. So, in the context of investment portfolios, a smaller standard deviation means less risk as it indicates more steady, predictable returns.

Step-by-step solution

Define Standard Deviation

The standard deviation is a statistical measurement in dispersion or volatility. It quantifies the dispersion of a data set or, in this case, the volatility of returns on a portfolio. The standard deviation tells you how much your outcomes (returns) deviate from the average return.

Correlation Between Standard Deviation and Risk

In financial terms, 'risk' generally refers to the likelihood that the actual return on an investment will be different than the expected return. A larger standard deviation (greater dispersion) represents greater variability in potential outcome; hence, more risk since returns can swing more drastically, either positively or negatively.

Role of Diversification

Diversification is the strategy of investing in a variety of assets to reduce risk. The more diverse a portfolio is, the less impact any single investment's performance will have on the overall portfolio. Diversification typically leads to a lower portfolio standard deviation, hence less risk, because the diverse investments likely won’t all perform poorly at the same time.

Practical Example

In the provided examples, the second portfolio, which was more diversified, had a lower standard deviation of returns (7.97%) compared to the less diversified first portfolio (9.26%). This means that, while the returns of the second portfolio may vary, those variations are likely to be less extreme than in the less diversified first portfolio, thus indicating less risk.