Risk and Return II

Foundations of Finance
Lecture 11-12: Risk and Return II

In the last lecture we talked about individual stocks. This lecture is more about portfolios of stocks.
To diversify their risks investors invest in many companies which together make their portfolio. The
expected return of the portfolio is the weighted average of the expected returns of the individual
stocks within the portfolio.
E  RP   E i xi Ri    Ex R 
i i i   x E R 
i i i


However the risk diversified also depends on the co-movement of different stocks. Co-movement
can be measured by co-variance.

Covariance:

It measures how two stocks move together. Calculating covariance from expected returns:

Cov(Ri ,R j )  E[(Ri  E[ Ri ]) (R j  E[ R j ])]

Calculating co-variance from historical data:
1
Cov(Ri ,R j )   (Ri,t  Ri ) (R j ,t  R j )
T  1 t
If the covariance is positive, the two stocks move together and if its negative, then the two stocks
move opposite to each other.

The calculation of covariance is affected by two factors – co-movement of the two stocks and the
volatility of the individual stock. To get rid of the volatility factor, we calculate correlation.

Correlation:
Cov(Ri ,R j )
Corr (Ri ,R j ) 
SD(Ri ) SD(R j )
Correlation of the stocks will always be between +1 and -1.

Two stock portfolio:

Variance:

Var (RP )  x12Var (R1 )  x22Var (R2 )  2 x1 x2Cov(R1 ,R2 )

Standard Deviation:
SD(RP )  Var (RP )

Efficient Portfolio: It is the portfolio whose return can’t be increased any further without increasing
the volatility.

Inefficient Portfolio: It is the portfolio whose return can be increased without affecting its volatility.
For a 2 stock portfolio with following graph is obtained when different combinations are tried: