risk and return in detail

1. Risk and Return

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

18. Efficient Frontier

19. Effect of diversification

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.

29. Security market line

30. Valuation using SML