3 - 1 Risk and Return in Capital Budgeting

Risk And Return of A Single Asset Risk refers to the variability of expected returns associated with a given security or asset. Return- Periodic cash receipts & Appreciation ( Depreciation in the price of the asset

3 - 3 Return of a Single Asset

If the price of a share on April 1 (current year) is Rs 25, the annual dividend received at the end of the year is Re 1 and the year-end price on March 31 is Rs 30, the rate of return = [Re 1 + (Rs 30 – Rs 25)]/Rs 25 = 0.24 = 24 per cent. The rate of return of 24 per cent has two components: (i) Current yield, i.e. annual income ÷ beginning price = Re 1/Rs 25 = 0.04 or 4 per cent and (ii) Capital gains/loss = (ending price – beginning price) ÷ beginning price = (Rs 30 – Rs 25)/ 25 = 0.20 = 20 per cent. Measurement of Risk The two major concerns of an investor, while choosing a security (asset) as an investment, are the expected return from holding the security and the risk that the realised return may fall short of the expected return. To obtain a more concrete measure of risk, two statistical measures of variability of return, namely, standard deviation and coefficient of variation, can be used.

Probability (Distribution) Probability distribution is a model that relates probabilities to the associated outcome. Probability is the chance that a given outcome will occur.

Table 2: Table 2: Expected Rates of Returns (Probability Distribution) Possible outcomes (1) Probability (2) Returns (per cent) (3) Expected returns [(2) × (3)] (4) Asset X Pessimistic (recession) Most likely (normal) Optimistic (boom) Asset Y Pessimistic (recession) Most likely (normal) Optimistic (boom) Based on the probabilities assigned (probability distribution of) to the rate of return, the expected value of the return can be computed. The expected rate of return is the weighted average of all possible returns multiplied by their respective probabilities. Thus, probabilities of the various outcomes are used as weights. The expected return,

Table 3: Standard Deviation of Returns Asset X i % % 16 (–2)% 0 2 4% % Asset Y (–8) Standard Deviation Standard deviation measures the dispersion around the expected value. Expected value of a return is the most likely return on a given asset/security.

Risk And Return of Portfolio

Risk and Return of Portfolio A portfolio means a combination of two or more securities (assets). A large number of portfolios can be formed from a given set of assets. Each portfolio has risk-return characteristics of its own. Portfolio Expected Return The expected rate of return on a portfolio is the weighted average of the expected rates of return on assets comprising the portfolio. Symbolically, the expected return for a n-asset portfolio is defined by Equation 5. E (r p ) = Σw i E (r i ) whereE (r p ) = Expected return from portfolio w i = Proportion invested in asset i E (r i ) = Expected return for asset i n = Number of assets in portfolio Example 2 Suppose the expected return on two assets, L (low-risk low-return) and H (high-risk high-return), are 12 and 16 per cents respectively. If the corresponding weights are 0.65 and 0.35, the expected portfolio return is = [0.65 × × 0.16] = or 13.4 per cent.

Portfolio Risk (Two-Asset Portfolio) Total risk is measured in terms of variance (σ 2, pronounced sigma square) or standard deviation (σ, pronounced sigma) of returns. The overall risk of the portfolio includes the interactive risk of an asset relative to the others, measured by the covariance of returns. The covariance, in turn, depends on the correlation between returns on assets in the portfolio. The total risk of a portfolio made up of two assets is defined by the Equation 6. σ 2 p = w 2 1 σ w 2 2 σ w 1 w 2 (σ 12 ) Alternatively, σ 2 p = (w 1 σ 1 ) 2 + (w 2 σ 2 ) 2 + 2w 1 w 2 (ρ 12 σ 1 σ 2 ) where σ 2 p = Var (r p ) or variance of returns of the portfolio w 1 = Fraction of total portfolio invested in asset 1 w 2 = Fraction of total portfolio invested in asset 2 σ 2 1 = Variance of asset 1 σ 1 = Standard deviation of asset 1 σ 2 2 = Variance of asset 2 σ 2 = Standard deviation of asset 2 σ 12 = Covariance between returns of two assets (= ρ 12 σ 1 σ 2 ) ρ 12 = Coefficient of correlation (pronounced Rho) between the returns of two assets.

Let us assume that standard deviations of assets L and H, of our Example 2 are 16 and 20 per cents respectively. If the coefficient of correlation between their returns is 0.6 and the two assets are combined in the ratio of 3:1, the expected return of the portfolio is determined as follows: E (r portfolio ) = w L E (r L ) + w H E (r H ) = (0.75 × 12%) + (0.25 × 16%) = 9.0% + 4.0% = 13 per cent The variance of the portfolio is given by: σ 2 p = (w 1 σ 1 ) 2 + (w 2 σ 2 ) w 1 w 2 ( ρ 12 σ 1 σ 2 ) = (0.75 × 16) 2 + (0.25 × 20) (0.75) (0.25) [(0.6) (16 × 20)] = (0.375)(192) = = 241 Thus, σ p = per cent The above discussion shows that the portfolio risk depends on three factors: (a) Variance (or standard deviation) of each asset in the portfolio; (b) Relative importance or weight of each asset in the portfolio; (c) Interplay between returns on two assets or interactive risk of an asset relative to other, measured by the covariance of returns.