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5.1 Risk Return Relationship
The most fundamental tenet of finance literature is that there is a tradeoff between risk and return. The riskreturn relationship requires that the return on a security should be commensurate with its riskiness. If the capital markets are operationally efficient, then all investment assets should provide a rate or return that is consistent with the risks associated with them. The risk and return are directly variable, i.e., an investment with higher risk should produce higher return.
The risk/return tradeoff could easily be called the "abilitytosleepatnight test." While some people can handle the equivalent of financial skydiving without batting an eye, others are terrified to climb the financial ladder without a secure harness. Deciding what amount of risk you can take while remaining comfortable with your investments is very important.
In the investing world, the dictionary definition of risk is the possibility that an investment's actual return will be different than expected. Technically, this is measured in statistics by standard deviation. Risk means you have the possibility of losing some, or even all, of your original investment.
Low levels of uncertainty (low risk) are associated with low potential returns. High levels of uncertainty (high risk) are associated with high potential returns. The risk/ return tradeoff is the balance between the desire for the lowest possible risk and the highest possible return. This is demonstrated graphically in the chart below. A higher standard deviation means a higher risk and higher possible return. The figure below represents the relationship between risk and return.
The slope of the Market Line indicates the return per unit of risk required by all investors. Highly riskaverse investors would have a steeper line, and vice versa. Yields on apparently similar stocks may differ. Differences in price, and therefore yield, reflect the market's assessment of the issuing company's standing and of the risk elements in the particular stocks. A high yield in relation to the market in general shows an above average risk element
Risk & return relationship of various securities
Given the composite market line prevailing at a point of time, investors would select investments that are consistent with their risk preferences. Some will consider lowrisk investments, while others prefer highrisk investments.
A common misconception is that higher risk equals greater return. The risk/return tradeoff tells us that the higher risk gives us the possibility of higher returns. But there are no guarantees. Just as risk means higher potential returns, it also means higher potential losses.
On the lower end of the scale, the riskfree rate of return is represented by the return on Treasury Bills of government securities, because their chance of default is next to nil. If the riskfree rate is currently 8 to 10 %, this means, with virtually no risk, we can earn 8 to 10 % per year on our money. The common question arises: who wants to earn 6% when index funds average 12% per year over the long run? The answer to this is that even the entire market (represented by the index fund) carries risk. The return on index funds is not 12% every year, but rather 5% one year, 25% the next year, and so on. An investor still faces substantially greater risk and volatility to receive an overall return that is higher than a predictable government security. This additional return is the risk premium, which in this case is 8% (12%  8%). Determining what risk level is most appropriate for you isn't an easy question to answer. Risk tolerance differs from person to person. The decision should depend on your goals, income and personal situation, among other factors.
5.2 Portfolio and Security Returns
A portfolio is a collection of securities. Since it is rarely desirable to invest the entire funds of an individual or an institution in a single security, it is essential that every security be viewed in a portfolio context. Thus, it seems logical that the expected return of a portfolio should depend on the expected return of each of the security contained in the portfolio. It also seems logical that the amounts invested in each security should be important. Indeed, this is the case.
The example of a portfolio with three securities shown below that illustrates this point.
Security and Portfolio Values
Security
(1) 
No. of shares
(2) 
Current Price per share
(3) 
Current Value
(4) 
Expected End of the period share value (5) 
Expected End of the Period Share Value (6) 
XYZ 
100 
15 
1500 
18 
1800 
ABC 
150 
20 
3000 
22 
3300 
EFG 
200 
40 
8000 
45 
9000 
KLM 
250 
25 
6250 
30 
7500 
NOP 
100 
12.5 
1250 
15 
1500 



20000 

23100 
Security and Portfolio ValueRelative
Security 
Current Value 
Proportion of current value of Portfolio 
Current Price per share 
Expected End of the period share value 
Expected Holding Period Value Relative 
Contribution to Portfolio Expected HoldingPeriod ValueRelative 
(1) 
(2) 
(3)=2/20000 
(4) 
(5) 
(6)= 5/4 
(7)=3*6 
XYZ 
1500 
0.0750 
15 
18 
1200 
0.0900 
ABC 
3000 
0.1500 
20 
22 
1000 
0.1650 
EFG 
8000 
0.4000 
40 
45 
1125 
0.4500 
KLM 
6250 
0.3125 
25 
30 
1200 
0.3750 
NOP 
1250 
0.0625 
12.5 
15 
1200 
0.0750 

20,000 
1.000 



1.155 
Security and Portfolio Holdingperiod Returns
Security (1) 
Proportion of current value of Portfolio (2) 
Expected Holding Period Return (%) (3) 
Contribution to Portfolio Expected Holding Period Return (%) (4)= 2*3 
XYZ 
0.0750 
20 
1.50 
ABC 
0.1500 
10 
1.50 
EFG 
0.4000 
12.5 
5.00 
KLM 
0.3125 
20 
6.25 
NOP 
0.0625 
20 
1.25 



15.50 
Since the portfolio's expected return is a weighted average of the expected returns of its securities, the contribution of each security to the portfolio's expected returns depends on its expected returns and its proportionate share of the initial portfolio's market value. Nothing else is relevant. It follows that an investor who simply wants the greatest possible expected return should hold one security. This should be the one that is considered to have the greatest expected return. Very few investors do this, and very few investment advisers would counsel such an extreme policy. Instead, investors should diversify, meaning that their portfolio should include more than one security. This is because diversification can reduce risk.
5.3 Risk and Return Calculation
Lets take an example of a single security also and understand its return calculation. The table below shows the average market price and dividend per share of SAIL Limited for the past 6 years:
Year 
Avg Market price 
Dividend per share 
2016 
50 
3 
2017 
55 
5 
2018 
60 
2 
2019 
70 
4 
2020 
65 
2 
2021 
80 
2 
So, avg return for SAIL Limited would be:
Year 
Avg Market price 
Capital gain (%) 
Dividend per share 
Dividend Yield (%) 
Rate of Return 
(1) 
(2) 
(3) 
(4) 
(5)=4/2 
(6)= 3+5 
2016 
50 
 
3 
6.00% 
 
2017 
55 
10.00% 
5 
9.09% 
19.09% 
2018 
60 
9.09% 
2 
3.33% 
12.42% 
2019 
70 
7.69% 
4 
5.71% 
13.41% 
2020 
65 
7.14% 
2 
3.07% 
4.07% 
2021 
80 
23.07% 
2 
2.50% 
20.57% 
Average Return= (19.09+12.42+13.414.07+20.57)/5= 12.28%
Lets calculate the standard deviation for SAIL Limited considering certain probabilities for occurrence of each of these returns
Year 
Rate of Return 
Probability 
Rate of Return Average Return 
(Rate of ReturnAvg Return)^2* P 
(1) 
(2) 
(3) 
(4) 
(5)= (4^2)*P 
2017 
19.09% 
0.35 
6.81 
16.210 
2018 
12.42% 
0.10 
0.14 
0.0019 
2019 
13.41% 
0.20 
1.13 
0.2552 
2020 
4.07% 
0.05 
16.35 
13.360 
2021 
20.57% 
0.30 
8.29 
20.634 


1.00 

50.447 
Average Return= 12.28%
Standard Deviation= √50.447 = 7.10%
5.4 Return Calculation of Portfolio ( Two Assets)
The expected return from a portfolio of two or more securities is equal to the weighted average of the expected returns from the individual securities.
Where,
ε(Rp)= Expected return from a portfolio of two securities
Wa= Proportion of funds invested in Security A
Wb= Proportion of funds invested in Security B
Ra = Expected return of Security A
Rb= Expected return of Security B
Wa+Wb=1
Lets take an example: Ms. Ridhi's portfolio consist of 6 securities and individual weight and return of each security is given below.
Security 
Proportion of Investment 
Return (%) 
Wipro 
10% 
18% 
ICICI Bank 
25% 
12% 
ITC 
8% 
22% 
Tata Motors 
30% 
15% 
HDFC Bank 
12% 
6% 
Eicher Motors 
15% 
8% 
The weighted avg return would be: (0.10*18)+(0.25*12)+(0.08*22)+(0.30*15)+(0.12*6)+(0.15*8)
= 12.98%
5.5 Return Calculation of Portfolio ( Two Assets)
The risk of a security is measured in terms of variance or standard deviation of its returns. The portfolio risk is not simply a measure of its weighted average risk. The securities that a portfolio contains are associated with each other. The portfolio risk also considers the covariance between the returns of the investment. Covariance of two securities is a measure of their comovement; it expresses the degree to which the securities vary together.
The standard deviation of a twoshare portfolio is calculated by applying formula given below:
The covariance of Security A and Security ( ) can be presented as follows:
CovAB = qA qB PAB
The diversification of unsystematic risk, using a twosecurity portfolio, depends upon the correlation that exists between the returns of those two securities. The quantification of correlation is done through calculation of correlation coefficient of two securities (rAB). The value of correlation ranges between  1 to 1; it can be interpreted as follows:
If
PAB = 1, No unsystematic risk can be diversified.
PAB =  1, All unsystematic risks can be diversified.
PAB = 0, No correlation exists between the returns of Security A and Security B.
The returns of Security of Wipro and Security of Infosys for the past five years are given below:
Year 
Wipro Return (%) 
Infosys Return (%) 
2017 
9 
10 
2018 
5 
6 
2019 
3 
12 
2020 
12 
9 
2021 
16 
15 
Mean Return & Standard Deviation of Wipro
Year 
Wipro Return (%) 
Mean Return Return 
(MeanReturn)^2 
2017 
9 
0 
0 
2018 
5 
4 
16 
2019 
3 
6 
36 
2020 
12 
3 
9 
2021 
16 
7 
49 

45 

110 
Mean Return= 45/5= 9%
Standard Deviation= √110= 10.49%
Mean Return & Standard Deviation of Infosys
Year 
Infosys Return (%) 
Mean Return Return 
(MeanReturn)^2 
2017 
10 
2 
4 
2018 
6 
14 
196 
2019 
12 
4 
16 
2020 
9 
1 
1 
2021 
15 
7 
49 

40 

266 
Mean Return= 40/5= 8%
Standard Deviation= √266= 16.31%
Analysis  Wipro has a higher historic level of return and lower risk as compared to Infosys
Covariance of Returns of Infosys & Wipro
Year 
Return A (%) 
Return B (%) 
(Mean of RA Return of RA) 
Mean of Rb Return of B 

(1) 
(2) 
(3) 
(4) 
(5) 
(6)= 4*5 
2017 
9 
10 
0 
2 
0 
2018 
5 
6 
4 
14 
56 
2019 
3 
12 
6 
4 
24 
2020 
12 
9 
3 
1 
3 
2021 
16 
15 
7 
7 
49 

Mean 9% 
Mean= 8% 


COVab=84 
P_{AB}= COV_{AB}/ q_{A }q_{B}= 84/(10.49*16.31)= 0.491
COV_{AB}= q_{A }q_{B }P_{AB}= 10.49*16.31*0.491= 84
Return of portfolio (Rp ) = (0.80 * 9) + (0.20* 8) = 7.2 + 1.6 = 8.8%
Risk of portfolio (q_{p} ) = (0.80^{2} *10.49^{2} ) + (0.20^{2} *16.31^{2} ) + (2 *0.80 * 0.20 * 10.49 * 16.31 * 0.491)
= (0.64 *110.04) + (0.04 * 266.02) + 26.88
= 70.43 + 10.64 + 26.88 = 107.95
(q_{p} ) = √107.95 = 10.39%