Corporate Finance II Lecture 04
Shama-e Zaheer

Risk and Return

Risk is the variability of returns from any asset. The greater the risk, the greater the required return from the asset.

Therefore, in order to find the required return from any asset we need to know its risk and match that risk to another asset (or portfolio of assets) with a known return and use that as the opportunity cost of capital for the risky asset.

Required Return, or, ri = Risk-free Rate (RFR) + Risk Premium (RP)

Measuring Risk
Calculate the standard deviation of returns to measure the variability, hence the risk of an asset.

Possible Return Probability of Occurrence (Project A) Probability of Occurrence (Project B)
-0.1 0.05 0.01
-0.02 0.1 0.03
0.04 0.2 0.16
0.09 0.3 0.6
0.14 0.2 0.16
0.2 0.1 0.03
0.28 0.05 0.01

Returns could also take continuous values, in which case, a normal distribution of returns may be assumed and probabilities associated with range of values may be calculated.

To compare the riskiness of alternatives of different expected returns, use Coefficient of Variation instead of standard deviation.

Inv A Inv B
Expected Return, R 0.08 0.24
Standard Deviation, σ 0.06 0.08
Coefficient of Variation, σ/R 0.75 0.33

Investors are generally risk-averse. Therefore, they would need to be compensated for risk through risk premia.

But remember that diversification reduces risk. Therefore, investors have to be compensated for the risk they cannot diversify away.

Stock 1 Stock 2
Stock 1 x12σ12 x1x2σ12 = x1x2ρ12σ1σ2
Stock 2 x1x2σ12 = x1x2ρ12σ1σ2 x22σ22 Table: Calculating Portfolio Variance, (add the boxes)

Therefore, a stock has two types of risks: i) Unique Risk, ii) Market Risk

 Unique risk may be diversified away.
 Market risk is the sensitivity of the portfolio return to market movements. The sensitivity of a stock to