Risk and Return I

Foundations of Finance
Lecture 9-10: Risk and Return I

Generally higher the risk, higher is the return desired on it. But the question arises how much the
investors demand in order to bear a certain level of risk. Throughout this lecture, we will be
assessing different methods of risk assessment.

1. Probabilistic approach:

A probability is assigned to all the returns and then the equivalent is calculated.

Expected Return  E  R   R
PR  R

Variance and Standard Deviation-

Variance and standard deviation both measure uncertainty in the measurements. Variance
measures the dispersion of the data relative to the mean and standard deviation is the square root
of mean. SD is also known as the volatility.

Var (R)  E  R  E  R     R  E  R 
2 2
PR 
  R


SD( R)  Var ( R)
One major problem with this approach is the measurement of the probabilities because it can be
very hard to assign a particular probability to a particular return.

2. Historical Data Approach:

For a given year, realized return is the sum of capital gain and dividend yield.
Divt  1  Pt  1 Divt  1 Pt  1  Pt
Rt  1   1  
Pt Pt Pt
Dividend Yield Capital Gain Rate
Over a period of time realized return:
1  Rannual  (1  RQ1 )(1  RQ 2 )(1  RQ3 )(1  RQ 4 )

This can also be referred to as geometric return. Average or arithmetic annual return is equal to:
1 1 T
R 
T
 R1  R2   RT    Rt
T t 1


Variance of the realized returns is equal to:
T

 R  R
1 2
Var (R) 
T  1
t
t 1