Learn About Measuring Risk & Return of Mutual Fund | Finschool (2022)

5.1 Risk Return Relationship

The most fundamental tenet of finance literature is that there is a trade-off between risk and return. The risk-return 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 trade-off could easily be called the "ability-to-sleep-at-night 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 trade-off 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.

Learn About Measuring Risk & Return of Mutual Fund | Finschool (2)

The slope of the Market Line indicates the return per unit of risk required by all investors. Highly risk-averse 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

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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 low-risk investments, while others prefer high-risk 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 risk-free 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 risk-free 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 Value-Relative

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 Holding-Period Value-Relative

(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 Holding-period 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+13.41-4.07+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 Return-Avg 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 co-variance between the returns of the investment. Covariance of two securities is a measure of their co-movement; it expresses the degree to which the securities vary together.

The standard deviation of a two-share 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 two-security 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

(Mean-Return)^2

2017

9

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

(Mean-Return)^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

Co-variance 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

2

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

PAB= COVAB/ qA qB= 84/(10.49*16.31)= 0.491

COVAB= qA qB PAB= 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 (qp ) = (0.802 *10.492 ) + (0.202 *16.312 ) + (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

(qp ) = 107.95 = 10.39%

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