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- 1. Portfolio Risk Lecture 14
- 2. Portfolio risk <ul><li>Though return of portfolio is the weighted average return of individual assets in the portfolio </li></ul><ul><li>But risk of a portfolio is not a weighted average risk of individual assets </li></ul><ul><li>Because overall risk is reduced by combining assets into one portfolio </li></ul>
- 3. Why risk decrease when we combine two or more assets <ul><li>Suppose that the following table shows expected return on PIA and POL shares </li></ul><ul><li>SD of PIA return = 9.2 </li></ul><ul><li>SD of POL return =7.63 </li></ul>Scenario PIA POL Averag Same oil price 10% 10% 10% Oil prices fall 20% 5% 12.5% Oil prices rise 2% 20% 11%
- 4. Interpretation <ul><li>If we invest only in PIA, our return may fluctuate by a value of 9.2% </li></ul><ul><li>Similarly if we invest only in POL, our return may fluctuate by a value of 7.63% </li></ul><ul><li>However, if we invest half of our funds in PIA and half in POL, fluctuation in our return will considerably decrease. </li></ul><ul><li>The return on combined portfolio may fluctuate by a value of 3.55% </li></ul>
- 5. Why the SD fell by combining two asset? <ul><li>Because when return on PIA fell, return on POL increased and vise versa </li></ul><ul><li>The negative effect of macro-economic variable (oil prices) on one security is offset by the positive effect on the return of other security </li></ul><ul><li>The average return on both of the securities is less volatile </li></ul>
- 6. What is necessary for combining securities to reduce risk? <ul><li>combine such stocks the return of which are affected in opposite direction from a change in the same economic variable </li></ul><ul><li>i.e stocks in our portfolio should have negative correlation </li></ul>
- 7. Portfolio Risk will not decrease <ul><li>When the stocks return move in the same direction by equal percentage(Perfect positive correlation) </li></ul><ul><li>i.e If changes in economic variables have negative effect on both of the stocks </li></ul>
- 8. Why risk falls in a portfolio? <ul><li>By combining negatively correlated stocks, we can remove the individual risks ( Unsystematic risk ) of the stocks </li></ul><ul><li>Example: POL has the risk of falling oil prices and PIA has the risk of rising oil prices </li></ul><ul><li>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 </li></ul><ul><li>However, all of market risk cannot be eliminated through diversification ( Systematic Risk ) </li></ul>
- 9. Risk Reduction with Diversification Number of Securities St. Deviation Market Risk Unique Risk
- 10. Co-variance <ul><li>To calculate portfolio risk, we need to know how stocks in the portfolio co-vary </li></ul><ul><li>Covariance is the extent to which two random variables move together over time. (Return of two stocks) </li></ul><ul><li>If it is positive, it means the variables move in the same direction </li></ul><ul><li>If it is zero, it means that there is no relationship </li></ul><ul><li>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) </li></ul>
- 11. Formula of covariance <ul><li>Covariance is the expected value of deviations from the mean </li></ul><ul><li>Covariance is useful in a sense that it shows whether the returns move in same direction or in opposite directions </li></ul><ul><li>The value of covariance in itself is less meaningful because you cannot compare it with anything </li></ul><ul><li>i.e you cannot say the value is higher, lower, or reasonable </li></ul>
- 12. To make covariance meaningful <ul><li>To make the covariance meaningful so that its value can be compared with other values, we make it a relative measure </li></ul><ul><li>The relative measure is correlation coefficient, denoted by rho = </li></ul>
- 13. Correlation Coefficient <ul><li>Correlation coefficient can vary from +1 to -1 </li></ul><ul><li>+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% </li></ul><ul><li>-1 means that if security A return increases by 100%, security B return will decrease by 100% </li></ul>
- 14. Calculating Portfolio Risk <ul><li>Risk of the porftolio is not the weighted average risk of the individual securities </li></ul><ul><li>Rather it is determined by three factors </li></ul><ul><ul><li>1.the SD of each security </li></ul></ul><ul><ul><li>2. the covariance between the securities </li></ul></ul><ul><ul><li>The weights of securities in the portfolio </li></ul></ul>
- 15. EXAMPLE <ul><li>Suppose POL gave you = 12.12% return </li></ul><ul><li>And PIA = 15.16% return </li></ul><ul><li>SD of POL = 21.58 and PIA = 25.97 </li></ul><ul><li>Correl coeff = .29 </li></ul><ul><li>Weights POL = 50% and PIA = 50% </li></ul><ul><li>What is the SD of the portfolio? </li></ul>
- 17. <ul><li>Suppose we invest 50% in PIA and 50% in POL, then what is the portfolio SD </li></ul>Scenario PIA POL Same oil price 10% 10% Oil prices fall 20% 5% Oil prices rise 2% 20%
- 19. What if we change weights? <ul><li>Which combination is superior: </li></ul>Portfolios PIA POL SD of Portfolio Return of Portfolio A 25% 75% 4.59% 11.4% B 50% 50% 3.55% 11.2% C 75% 25% 5.71% 10.9% D 100% 0 9.01% 10.67%

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