Risk and return part 2
- 2. Portfolio A portfolio comprises of multiple securities. Serves as a hedge against adverse conditions
- 3. Portfolio Return The return on portfolio is determined by the weighted average of the returns of individual securities. Weight of an individual security in the portfolio is the percentage of that security in the portfolio
- 4. Portfolio return Two securities TCS and HCL with expected returns of 10% and 20% respectively constitute a portfolio. What would be the return Of the portfolio if the proportion of security TCS and HCL in the Portfolio is 10% and 90% respectively.
- 6. What would be the return of the portfolio if the proportion of security TCS and HCL in the portfolio is given below respectively. % of A in portfolio % of B in portfolio 10% 90% 20% 80% 30% 70% 40% 60% 50% 50% 60% 40% 70% 30% 80% 20% 90% 10% 100% 0%
- 7. % of TCS in portfolio % of HCL in portfolio 10% 90% 20% 80% 30% 70% 40% 60% 50% 50% 60% 40% 70% 30% 80% 20% 90% 10% 100% 0%
- 8. Next example Find the portfolio return for the following scenarios. Equal amount is invested in all three securities. Scenarios Prob. of scenarios Return of RIL Return of CIL Return of HCL Boom 0.3 0.15 0.18 0.20 Stagnant 0.5 0.10 0.12 0.12 Decline 0.2 -0.03 0.05 0.08
- 9. The portfolio return would be calculated by taking the weighted average of returns of securities comprising the portfolio. Where, weights of individual securities are the proportional contribution of that security in the portfolio. Scenarios Prob. of scenarios Return of RIL Return of CIL Return of HCL Boom 0.3 0.15 0.18 0.20 Stagnant 0.5 0.10 0.12 0.12 Decline 0.2 -0.03 0.05 0.08 Expected returns 0.089 0.124 0.136
- 10. Portfolio Risk Calculating risk of a portfolio is a little different than calculating Return of a portfolio. Unlike portfolio return, which is the weighted average of returns of assets in the portfolio. Portfolio risk is NOT simply the weighted average of risks of assets in the portfolio. While calculating risk of the portfolio, the co-movement of securities with each other also plays a crucial role that needs to be taken into account
- 11. Formula for calculating portfolio risk w1σ1 w2σ2 w1σ1 w1 2σ1 2 w1w2σ1σ2 w2σ2 w1w2σ1σ2 w2 2σ2 2 w1σ1 w2σ2 w3σ3 w1σ1 w1 2σ1 2 w1w2σ1σ2 w1w3σ1σ3 w2σ2 w1w2σ1σ2 w2 2σ2 2 w2w3σ2σ3 w3σ3 w1w3σ1σ3 w2w3σ2σ3 w3 2σ3 2
- 12. Two securities 1 and 2 with expected returns of 10% and 20% respectively and standard deviation of 15% and 25% respectively constitute a portfolio. What would be the return of the portfolio if the proportion of security 1 and 2 in the portfolio is 10% and 90% respectively and the coefficient of correlation is 0.35.
- 14. Two securities A and B with expected returns of 10% and 20% respectively and standard deviation of 15% and 25% respectively constitute a portfolio. What would be the return and risk of the portfolio if the proportion of security A and B in the portfolio is in varying proportions respectively and the coefficient of correlation is: 1. +1 2. 0.5 3. 0 4. -0.5 5. -1
- 15. Effect of diversification ρ=+1 Sec A (%) Sec B (%) R_port (%) σ_port (%) 1 0 0.1 0.0225 0.9 0.1 0.11 0.0256 0.8 0.2 0.12 0.0289 0.7 0.3 0.13 0.0324 0.6 0.4 0.14 0.0361 0.5 0.5 0.15 0.04 0.4 0.6 0.16 0.0441 0.3 0.7 0.17 0.0484 0.2 0.8 0.18 0.0529 0.1 0.9 0.19 0.0576 0 1 0.2 0.0625 ρ=0.5 Sec A (%) Sec B (%) R_port (%) σ_port (%) 1 0 0.1 0.0225 0.9 0.1 0.11 0.0222 0.8 0.2 0.12 0.0229 0.7 0.3 0.13 0.0245 0.6 0.4 0.14 0.0271 0.5 0.5 0.15 0.0306 0.4 0.6 0.16 0.0351 0.3 0.7 0.17 0.0405 0.2 0.8 0.18 0.0469 0.1 0.9 0.19 0.0542 0 1 0.2 0.0625
- 16. Effect of diversification ρ=0 Sec A (%) Sec B (%) R_port (%) σ_port (%) 1 0 0.1 0.0225 0.9 0.1 0.11 0.0189 0.8 0.2 0.12 0.0169 0.7 0.3 0.13 0.0167 0.6 0.4 0.14 0.0181 0.5 0.5 0.15 0.0213 0.4 0.6 0.16 0.0261 0.3 0.7 0.17 0.0327 0.2 0.8 0.18 0.0409 0.1 0.9 0.19 0.0509 0 1 0.2 0.0625 ρ=-0.5 Sec A (%) Sec B (%) R_port (%) σ_port (%) 1 0 0.1 0.0225 0.9 0.1 0.11 0.0155 0.8 0.2 0.12 0.0109 0.7 0.3 0.13 0.0088 0.6 0.4 0.14 0.0091 0.5 0.5 0.15 0.0119 0.4 0.6 0.16 0.0171 0.3 0.7 0.17 0.0248 0.2 0.8 0.18 0.0349 0.1 0.9 0.19 0.0475 0 1 0.2 0.0625
- 17. Effect of diversification ρ=-1 Sec A (%) Sec B (%) R_port (%) σ_port (%) 1 0 0.1 0.0225 0.9 0.1 0.11 0.0121 0.8 0.2 0.12 0.0049 0.7 0.3 0.13 0.0009 0.6 0.4 0.14 0.0001 0.5 0.5 0.15 0.0025 0.4 0.6 0.16 0.0081 0.3 0.7 0.17 0.0169 0.2 0.8 0.18 0.0289 0.1 0.9 0.19 0.0441 0 1 0.2 0.0625
- 20. Portfolio Beta Portfolio beta is the beta (relative risk) of the Portfolio. It is calculated just like portfolio return. It is calculated as the weighted average of the individual securities comprising the portfolio. The weight of individual security is the proportional contribution of that security in the portfolio.
- 21. Portfolio Beta A portfolio comprises of two securities A and B with their weights being 40% and 60%. The beta for A and B are 0.8 and 1.6 respectively.
- 22. Lines Characteristic Line Capital Allocation Line Capital Market Line Security Market Line (Graphical representation for CAPM)
- 23. Characteristic line A characteristic line is a straight line formed using regression analysis that summarizes a particular security's systematic risk (Beta) and rate of return. The characteristic line is also known as the security characteristic line (SCL). The y-axis on the chart measures the excess return of the security. Excess return is measured against the risk-free rate of return. The x axis on the chart measures the market's return in excess of the risk free rate. This line shows the security's performance versus the market's performance.
- 25. Capital allocation line The locus of portfolios constructed by adjusting the proportions of wealth in risk free asset and risky asset.
- 27. Capital market line The capital market line (CML) represents portfolios that Optimally combine risk and return. The capital market line (CML) represents portfolios that optimally combine risk and return. CML is a special case of the CAL where the risky portfolio is the market portfolio. Thus, the slope of the CML is the sharpe ratio of the market portfolio. The intercept point of CML and efficient frontier would result in the most efficient portfolio called the tangency portfolio. As a generalization, buy assets if sharpe ratio is above CML and sell if sharpe ratio is below CML.