Page 80 - DMGT405_FINANCIAL%20MANAGEMENT

Financial Management

Notes n
Of course   1 which represents that 100 per cent of portfolio assets must be included in this
i 1

computation.

Portfolio Risk – Two Asset Case
Individual assets or securities are more risky than portfolio. How is the risk of portfolio measured?
As discussed earlier risk is measured in terms of variance in standard deviation. The standard
deviation of a portfolio’s return is found by applying the formula for standard deviation of a
single asset.

Example: There are two investment opportunities A and B

The expected rate of return, variance and standard deviation of A are:
Return = 0.5 × 40 + 0.5 × 0 = 20%
2
2
Standard Deviation 2 = 0.5 (40 – 20) + 0.5 (0 – 20) = 400
Standard Deviation = 400  20%
And of B

Return = 0.5 × 40 + 0.5 × 0 = 20%
2
2
Standard Deviation 2 = 0.5 (0 – 20) + 0.5 (40 – 20) = 400
Standard Deviation = 400  20%
Both A and B have the same expected rate of return (20 per cent) and same variance (400) and
Standard Deviation (20 per cent). Thus, they are equally risky.
If the portfolio consisting of equal amount of A and B is constructed, the portfolio return would
be 0.5 × 20 + 0.5 × 20 = 20%, same as the expected return from individual securities but without
risk; why? If the economic conditions are good, then A would yield 40 per cent and zero and the
portfolio return will be 0.5 × 40 + 0.5 × 0 = 20%.
When the economic conditions are bad, then A’s return will be zero and B’s 40 per cent and the
portfolio return will be the same 0.5 × 0 + 0.5 × 40 = 20%.
Thus, by investing equal amount in both A and B, the investor is able to eliminate the risk
altogether and assumed of a return of 20 per cent with a 0.5 x 20 + 0.5 x 20 = 20%, same as the
expected return from individual securities but without risk; why? If the economic conditions are
good, then A would yield 40 per cent and zero and the portfolio return will be 0.5 × 40 + 0.5 × 0
= 20%.
When the economic conditions are bad, then A’s return will be zero and B’s 40 per cent and the
portfolio return will be the same 0.5 × 0 + 0.5 × 40 = 20%.
Thus, by investing equal amount in both A and B, the investor is able to eliminate the risk
altogether and assumed of a return of 20 per cent with a zero standard deviation.

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