Rate of Return

The rate of return is the gain or loss on an investment over a period, expressed as a proportion of the amount invested. The rate of return is a central concept in finance and in the analysis of investment.

Definition

The rate of return is calculated as the change in the value of the investment plus any income received, divided by the initial value. For a share, the return comprises the change in the price and the dividend. For a bond, it comprises the change in the price and the coupon.

The return may be measured over different periods, including a day, a month, or a year. The returns over different periods can be combined to compute the return over a longer period, using the geometric mean.

The return may be nominal, measured in current prices, or real, adjusted for inflation. The real return is the relevant measure for the assessment of the purchasing power of the investment.

Expected and Required Return

The expected return is the average of the possible returns, weighted by their probabilities. It is the measure that investors use in assessing the attractiveness of an investment, though it is not directly observable.

The required return is the minimum return that investors demand to hold the asset. It reflects the risk-free rate and a premium for the risk of the asset. The difference between the expected return and the required return determines whether the investment is attractive.

The relationship between the expected return and the risk of an asset is central to asset pricing. The models of asset pricing, including the capital asset pricing model, specify how the expected return depends on the risk of the asset.

Measurement

The measurement of the rate of return requires data on the prices and the income of the asset. The data are available for many assets, though the measurement of the return on some assets, including real estate and private equity, is more difficult.

The measurement must account for the costs of the transaction, including the commissions and the taxes, which reduce the net return. The measurement must also account for the timing of the cash flows, which affects the return.

The returns are used in the analysis of the performance of investments and of the efficiency of markets. The comparison of the returns of different assets informs the analysis of the risk premium and of the behaviour of investors.

Applications

The rate of return is used in the evaluation of investment projects, where the internal rate of return is compared with the cost of capital. It is used in the analysis of the performance of portfolios and of the skill of managers.

The rate of return is also used in the analysis of the economy, where the return on capital is a determinant of investment and of growth. The measurement of the return on capital informs the analysis of the distribution of income and of the effects of policy.

The Components of the Return

The return on an investment comprises the income that it generates and the change in its value. For a share, the income is the dividend, and the change in the value is the capital gain or loss.

The total return is the sum of the two components, expressed as a proportion of the initial investment. The decomposition of the return into the income and the capital components informs the analysis of the sources of the return and of the behaviour of the prices.

The return may be measured over different horizons, and the components may differ. Over the long run, the income component is a larger share of the total return, while over the short run the capital component may dominate.

The Risk Premium

The risk premium is the excess return that the investors require to hold a risky asset instead of a risk-free asset. The premium compensates the investors for the risk that they bear.

The premium is a central concept in the asset pricing, and it is estimated from the difference between the return on the risky assets and the return on the risk-free assets. The estimates vary and are subject to the uncertainty.

The premium is also a central concept in the analysis of the cost of capital, since the cost of the equity of a firm reflects the risk premium that the investors require. The design of the investment decisions and of the capital structure depends on the premium.

The Historical Returns

The historical returns on the major asset classes have been documented over long periods. The returns on the equity have exceeded the returns on the bonds and on the bills, and the difference is the equity premium.

The equity premium puzzle refers to the finding that the historical premium is larger than the standard models predict, given the risk aversion of the investors. The puzzle has been explained by the risk of the rare disasters, by the behaviour of the investors, and by the other factors.

The analysis of the historical returns informs the understanding of the behaviour of the markets and the design of the portfolios. The returns also inform the assumptions about the future returns, though the past performance is not a guarantee of the future.

Summary

The rate of return is the gain on an investment over a period, comprising the income and the capital components. The analysis of the components, of the risk premium, and of the historical returns informs the understanding of the investment and of the asset pricing.

See also

• Financial Economics
• Cost Accounting
• Financial Asset