1. Portfolio Risk
Lecture 14

2. Portfolio risk
Though return of portfolio is the weighted average return of individual assets in the portfolio
But risk of a portfolio is not a weighted average risk of individual assets
Because overall risk is reduced by combining assets into one portfolio

3. Why risk decrease when we combine two or more assets
Suppose that the following table shows expected return on PIA and POL shares
SD of PIA return = 9.2
SD of POL return =7.63
Scenario
PIA
POL
Averag
Same oil price
10%
Oil prices fall
20% 5%
12.5%
Oil prices rise 2%
11%

4. Interpretation
If we invest only in PIA, our return may fluctuate by a value of 9.2%
Similarly if we invest only in POL, our return may fluctuate by a value of 7.63%
However, if we invest half of our funds in PIA and half in POL, fluctuation in our return will considerably decrease.
The return on combined portfolio may fluctuate by a value of 3.55%

5. Why the SD fell by combining two asset?
Because when return on PIA fell, return on POL increased and vise versa
The negative effect of macro-economic variable (oil prices) on one security is offset by the positive effect on the return of other security
The average return on both of the securities is less volatile

6. What is necessary for combining securities to reduce risk?
combine such stocks the return of which are affected in opposite direction from a change in the same economic variable
i.e stocks in our portfolio should have negative correlation

7. Portfolio Risk will not decrease
When the stocks return move in the same direction by equal percentage(Perfect positive correlation)
i.e If changes in economic variables have negative effect on both of the stocks

8. Why risk falls in a portfolio?
By combining negatively correlated stocks, we can remove the individual risks (Unsystematic risk) of the stocks
Example: POL has the risk of falling oil prices and PIA has the risk of rising oil prices
By combining these two stocks, reduction in return in one stock due to change in oil price is compensated by increase in return of the other stock
However, all of market risk cannot be eliminated through diversification (Systematic Risk)

9. Risk Reduction with Diversification
Number of Securities
St. Deviation
Market Risk
Unique Risk

10. Co-variance
To calculate portfolio risk, we need to know how stocks in the portfolio co-vary
Covariance is the extent to which two random variables move together over time. (Return of two stocks)
If it is positive, it means the variables move in the same direction
If it is zero, it means that there is no relationship
Positive covariance of returns means that a change in macro economic variable (e.g oil prices) causes similar change in the returns of two stocks (e.g POL and OGDC)

11. Formula of covariance
Covariance is the expected value of deviations from the mean
Covariance is useful in a sense that it shows whether the returns move in same direction or in opposite directions
The value of covariance in itself is less meaningful because you cannot compare it with anything
i.e you cannot say the value is higher, lower, or reasonable

12. To make covariance meaningful
To make the covariance meaningful so that its value can be compared with other values, we make it a relative measure
The relative measure is correlation coefficient, denoted by rho =

13. Correlation Coefficient
Correlation coefficient can vary from +1 to -1
+1 means that the return on two securities are perfectly positvely correlated. If there is 100 positive change in security A return, the security B return will also increase by 100%
-1 means that if security A return increases by 100%, security B return will decrease by 100%

14. Calculating Portfolio Risk
Risk of the porftolio is not the weighted average risk of the individual securities
Rather it is determined by three factors
1.the SD of each security
2. the covariance between the securities
The weights of securities in the portfolio

15. EXAMPLE Suppose POL gave you = 12.12% return And PIA = 15.16% return
SD of POL = and PIA = 25.97
Correl coeff = .29
Weights POL = 50% and PIA = 50%
What is the SD of the portfolio?

17. Scenario
PIA
POL
Same oil price
10%
Oil prices fall
20% 5%
Oil prices rise 2%
Suppose we invest 50% in PIA and 50% in POL, then what is the portfolio SD

19. What if we change weights?
Which combination is superior:
Portfolios
PIA
POL
SD of Portfolio
Return of Portfolio A
25%
75%
4.59%
11.4% B
50%
3.55%
11.2% C
5.71%
10.9% D
100%
9.01%
10.67%