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Portfolio Risk

Portfolio Risk . Lecture 14. 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.

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Portfolio Risk

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  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

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

  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 = 21.58 and PIA = 25.97 • Correl coeff = .29 • Weights POL = 50% and PIA = 50% • What is the SD of the portfolio?

  16. Suppose we invest 50% in PIA and 50% in POL, then what is the portfolio SD

  17. What if we change weights? • Which combination is superior:

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