Investment Portfolio Management : Investment Portfolio Management Presented by: CA Tarun Mahajan Prepared by: CA Tarun Mahajan
Required Rate of Return : Required Rate of Return Required rate of return, i.e., expectations of an investor is a function of the following factors:
Real risk free rate of return
Inflation premium
Risk premium Prepared by: CA Tarun Mahajan
Real Risk Free Rate of Return : Real Risk Free Rate of Return It is the minimum expectation for return of an investor even in there is no inflation and no risk.
It is dependent upon the following:
Subjective factor: It can also be termed as compensation for deferment of consumption. if investor assigns more preference to current consumption then he will demand more RRFR for investment.
Objective factor: If the economy is growing, there will be more demand for fund hence higher RFRR. Prepared by: CA Tarun Mahajan
Nominal Risk Free Rate of Return : Nominal Risk Free Rate of Return It includes the effect of inflation.
(1+RFRnominal)=(1+RFRreal) (1+IP) or
If Real RFR is 6% and inflation premium is 4%, nominal RFR is 10.24% Prepared by: CA Tarun Mahajan
Risk Premium : Risk Premium An investor may require risk premium for the following risk:
Business Risk: depends upon the nature of firm’s business
Financial Risk: depends upon firms’ capital structure
Liquidity Risk: uncertainty of nearness to cash.
Exchange Rate Risk: It exists in case of foreign currency investments
Country risk: change in political or economic environment. Prepared by: CA Tarun Mahajan
Security Market Line : Security Market Line E(R) = RFR+ ß[E(Rmkt) –RFR]
E(R) = Expected Return
RFR = Nominal Risk free rate
E(Rmkt) = Return on well diversified market portfolio (return in equilibrium)
E(Rmkt) –RFR = Risk premium on market portfolio.
ß = Index of systematic risk.
E(R) = 9+ (15-9) 2 = 9+12 = 21%
Above equation is called equation of SML. Prepared by: CA Tarun Mahajan
Security Market Line : Security Market Line Systematic Risk (ß) Expected Return E(R) Security Market Line 1 E(Rmkt) 0 RFR Prepared by: CA Tarun Mahajan
Movement along SML : Movement along SML Systematic Risk (ß) Expected Return E(R) Security Market Line RFR More Risk Less Risk On SML when we move to right side, it indicates more risky security hence more expected rerun and vice versa. Prepared by: CA Tarun Mahajan
Shift of SML : Shift of SML Systematic Risk (ß) Expected Return E(R) Security Market Line 0 This indicates increase in nominal risk free rate of return. It is either due to increase in Real RFR or increase in inflation rate. Prepared by: CA Tarun Mahajan
Change in Slope of SML : Change in Slope of SML Systematic Risk (ß) Expected Return E(R) Security Market Line 0 Changing slope of SML indicates change in risk taking capacity of investors. Steeper slope indicates that investors are more risk averse now hence they require more premium for bearing same risk. Prepared by: CA Tarun Mahajan
SML : Conclusion : SML : Conclusion Movement along SML indicates a change in the systematic risk of a particular investment
Parallel shift in the SML change in Nominal risk free rate of return
Change in slope of SML indicates change in investors’ risk appetite. Prepared by: CA Tarun Mahajan
Security Below/Above SML : Security Below/Above SML Any point on SML indicates ideal expectation of investors.
If a security lie on SML. It means that actual expectation is equal to ideal expectation means the security is fairly priced.
If a security lie above SML. It means that actual expectation is more than ideal expectation means the security is under valued. It is recommended to buy the security
If a security lie below SML. It means that actual expectation is less than ideal expectation means the security is over valued. It is recommended to sell the security Prepared by: CA Tarun Mahajan
Security Below/Above SML : Security Below/Above SML Systematic Risk (ß) Expected Return E(R) Security A (Overvalued) Ideal Actual Security B (Undervalued) Security C (Fairly Priced) Prepared by: CA Tarun Mahajan
Slide 14 : Analysis of Risk Prepared by: CA Tarun Mahajan
Systematic & Unsystematic Risk : Systematic & Unsystematic Risk Risk means uncertainty of returns.
Total risk of a security can be classified into two parts namely, systematic risk and unsystematic risk.
Systematic Risk: It is a market related risk. it arises on account of the economy-wide uncertainties and affects all the securities in the market and not to any particular security. This is an unavoidable risk.
Unsystematic Risk: It is a company specific risk which affects a particular company only and not to the whole economy. This risk can be eliminated by diversification. Prepared by: CA Tarun Mahajan
Effect of diversification : Systematic Risk Effect of diversification A B AB Time Return No. of Securities Risk Unsystematic Risk We can observe that unsystematic risk can be avoided by diversification. Hence investor will not get any risk premium for bearing unsystematic risk.
For effective diversification one need not to hold entire assets in the world. Holding a few negatively correlated securities will reduce the unsystematic risk Prepared by: CA Tarun Mahajan
Risk & Return : Risk & Return Presented by: CA Tarun Mahajan Prepared by: CA Tarun Mahajan
Single Security: Expected Rate of Return : Single Security: Expected Rate of Return From Historical data
E(R)= (R1+R2+R3+……+Rn)/ n
Here Rn mean return for nth year.
Example: Calculate expected return, given return for last four year: 10%,-2%,15%,8%. Answer is 7.75%.
From Expected data
E(R)=R1P1+R2P2+………+RnPn
R1 means return when economy is in state 1.
Example: Given expected return of 10%, 12% and 14% with respective probability of .25, .50 & .25. Answer 12% Prepared by: CA Tarun Mahajan
Single Security: Risk : Single Security: Risk With Historical data risk is:
With Expected Data
In the previous example calculate risk of the portfolio. Prepared by: CA Tarun Mahajan
Two Security Portfolio: Risk & Return : Two Security Portfolio: Risk & Return Return of two security portfolio is equal to weighted average of return of individual securities.
Rp = R1W1+R2W2
Risk of a two security portfolio is:
Calculate risk & return for a portfolio of two securities A & B if their respective returns are 12 & 18 and risks are 16 & 24 and correlation is -0.6, if they are in the proportion of 70:30. Prepared by: CA Tarun Mahajan
Effect of correlation : Effect of correlation If r =1
If r = -1
If r = 0
We can make infinite combinations from two securities by varying their weights.
In the previous example if we assume different correlation, like +1, -1, +0.75, +0.5 etc. then the results come out. Prepared by: CA Tarun Mahajan
Slide 22 : Weights Portfolio Portfolio Risk (%)
---------------- Return ---------------------------------------------
C D (%) Cor=+1 Cor=-1 Cor=+0.75 Cor=+0.5
100 0 12.00 16.00 16.00 16.00 16.00
90 10 12.60 16.80 12.00 16.28 15.74
80 20 13.20 17.60 8.00 16.70 15.76
70 30 13.80 18.40 4.00 17.30 16.06
60 40 14.40 19.20 0.00 17.96 16.63
50 50 15.00 20.00 4.00 18.76 17.44
40 60 15.60 20.80 8.00 19.66 18.45
30 70 16.20 21.60 12.00 20.65 19.64
20 80 16.80 22.40 16.00 21.70 20.98
10 90 17.40 23.20 20.00 22.82 22.44
0 100 18.00 24.00 24.00 24.00 24.00 Prepared by: CA Tarun Mahajan
Slide 23 : Risk Return D C r=+1 Risk Return D C r=-1 Risk Return D C r=-.75 Return D C r=.75 Risk Will invest Won’t invest Prepared by: CA Tarun Mahajan
Three Security Portfolio : Three Security Portfolio Return: Rp = R1W1+R2W2+R3W3
Risk: Prepared by: CA Tarun Mahajan
Harry Markowitz Curve(Risk & Return of n security portfolio) : Harry Markowitz Curve(Risk & Return of n security portfolio) Risk Return Efficient Frontier C B A Every point in this area is portfolio which contains a combination of risk bearing securities. But it does not include any risk free security. Prepared by: CA Tarun Mahajan
Capital Market Line (CML) : Capital Market Line (CML) Return Risk CML M Lending Borrowing RFR CML is a straight line, which begins at RFR at which is tangent to efficient frontier.
Every point falling on CML is portfolio consisting of risk free and risk bearing securities.
Point M can be assumed to be market portfolio. Prepared by: CA Tarun Mahajan
CML: Equation : CML: Equation CML is series of portfolios consisting of risk free and risk bearing securities (market portfolio) in various proportions.
We know Rp = R1W1+R2W2
E(Rp)= RFR (1-Wm)+E(Rm)Wm
E(Rp)= RFR + [E(Rm)-RFR]Wm
Also if one of the securities is risk free (s1=0) hence sp=smWm Wm=sp/sm
Hence Equation for CML is
E(Rp)= RFR + [E(Rm)-RFR] sp/sm Prepared by: CA Tarun Mahajan
Indifference Curves : Indifference Curves CAPM assumes that all the investors are risk averse. It means that they prefer lower risk to higher risk.
It means to motivate them to take higher risk a disproportionately higher return will have to be offered to them.
Also investor tries to maximize his satisfaction (utility). Means for a given level of risk he will prefer more and more return. Prepared by: CA Tarun Mahajan
Indifference Curves : Indifference Curves Risk Return 1 3 2 Prepared by: CA Tarun Mahajan
Locating the optimal portfolio : Locating the optimal portfolio Risk Return CML Optimal Portfolio An investor can park his fund anywhere on the CML.
But to get highest satisfaction one should invest money where his indifference curve is tangent to CML Prepared by: CA Tarun Mahajan
Characteristic Line : Characteristic Line It the regression line taking return on market portfolio on X-axis and actual return on investor’s portfolio on Y-axis.
Equation for CL is Ri,t=?+ß R(mkt,t) +et
ß is the slope of CL and ? is the intersection of CL on Y-axis.
This equation is formed from historical data and is used to predict portfolio return, given return on market. Prepared by: CA Tarun Mahajan