VALUATION OF RISK AND RETURN IN MUTUAL FUND

PRESENTED BY

Anjali Agarwal – 1

Jasna Dolaramani – 7

Roshni Gandhi – 9

Anisha Lulla – 22

Deepika Malani – 23

Juhaina Khan – 41

Darshit Thakkar - 49

ACKNOWLEDGEMENT

We would like to thank Ms. Sanchita Roy, for giving

us this wonderful opportunity to work on this topic.

It was an amazing experience to work on the same

and grow our knowledge beyond books.

And we are honored to share the same with

our fellow batch mates.

INDEX

WHAT IS MUTUAL FUND ?

• Working of a mutual fund

RISK AND RETURN

• The dilemma faced

• Determine the level of risk

• Categorized as systematic and non systematic

risk

• To focus on portfolio rather than individual

assets

RISK VS RETURNS

• What is Mean?• Formula

Where:

(sometimes call the X-bar) is the symbol for the mean.

(the Greek letter sigma) is the symbol for summation.X is the symbol for the scores.N is the symbol for the number of scores.

RETURNS ON MUTUAL FUND

COMPOUND ANNUAL GROWTH RATE • Formula

CAGR = ( EV / BV)1 / n – 1

Where:EV = Investment's ending valueBV = Investment's beginning valuen = Number of periods (months, years, etc.)

Absolute Return or Point to Point Returns :

Absolute returns = 100* (Selling Price – Cost Price)/ (Cost Price)

• Formula

β = Covariance of Market Return with Stock Return

Variance of Market Return

β=Cov(R1 Rm)/σ2mWhere : Cov (R1 Rm) = covariance between the return on security i and the return on market portfolio.

σ2m = variance of return on the market portfolio=Rm-Rm2/(n-1)

• Formula

RISK ON MUTUAL FUND1. Beta

2. Standard Deviation

• Formula

PERFORMANCE MEASURES

• SHARPE RATIOa) Risk Measure. b) Formula: R-Rf/σWhere, R = Average Return Rf = Risk free rate σ = Standard Deviation.

PERFORMANCE MEASURES

• TREYNOR MEASUREa) Treynor’s Objective.b) Components of Risk.c) Security Market Line.d) Formula: R-Rf/βWhere, R = Average Return Rf = Risk free rate β = Beta

PERFORMANCE MEASURES

• JENSEN MEASURE:a) Capital Asset Pricing Model.b) Relationship between Risk and Expected Return.c) Formula: Rp = Ki + Bp(Rm-Ki)Where, Rp = Expected return of a portfolio Ki= Risk free rate of return Bp= Beta of a portfolio Rm= Expected return on market indexReal return = Average return - CAPM

CALCULATION OF RISK AND RETURN

CALCULATION OF RISK

Standard Deviation

The rate of return on stock X under different states of economy is presented below along with the probabilities of the occurrence of each state of the economy :

Boom Normal Recession

Probability of occurrence 0.4 0.3 0.3

Rate of Return on stock X 40 30 20

Calculation of the expected rate of return and standard deviation of return of stock X .

Solution :

Calculation of Expected Rate of Return :

State of Economy Probability

Rate of Return (X) Expected Return (X)

Boom 0.4 40 16

Normal 0.3 30 9

Recession 0.3 20 6

Expected Rate of Return ( XN ) 31

Calculation of the Standard Deviation on stock ‘X’

State of Economy

Xi (Xi – ‾Xi) (Xi – ‾Xi)² P Pi (Xi – ‾Xi)²

Boom 40 9 81 0.4 32.4

Normal 30 -1 1 0.3 0.3

Recession 20 -11 121 0.3 36.3

69

Standard Deviation = ξ69 = 8.30.

Calculate the beta value from the following information

Year Return on Security Return on Market Portfolio

1 10 12

2 12 10

3 13 10

4 10 12

5 8 15

6 11 14

7 16 20

8 12 15

9 18 20

10 20 22

Solution :

Calculation of Beta

COV (Ri – Rm) = Σ ( Ri – Ri‾ ) ( Rm – Rm‾ )² / n – 1

COV (Ri Rm) = 114 / 9 = 12.67

m = Σ ( Rm – Rm‾ )² / n – 1

m = 168 / 9 = 18.67

β = COV (Ri Rm) / m

β = 12.67 / 18.67 = 0.68 .

Year Ri Rm (Ri – Ri ‾) (Rm – Rm‾) (Ri – Ri‾) (Rm – Rm‾) (Rm – Rm‾)²

1 10 12 -3 -3 9 9

2 12 10 -1 -5 5 25

3 13 10 0 -5 0 25

4 10 12 -3 -3 9 9

5 8 15 -5 0 0 0

6 11 14 -2 -1 2 1

7 16 20 3 5 15 25

8 12 15 -1 0 0 0

9 18 20 5 5 25 25

10 20 22 7 7 49 49

n = 0 130 150 Ri= 13 Rm = 15 114 168

Calculation of Returns

Absolute return or Point to Point Returns :

Absolute return is the increase or decrease that an investment achieves over a given period of time expressed in percentage terms. It’s calculated as follows:

Absolute returns = 100* (Selling Price – Cost Price)/ (Cost Price)

For example you invested in asset in January 2005 at a price of Rs 12000. And you sold the investment in January 2012 at the cost of Rs 3200. Absolute returns in this case will be:

Absolute returns = 100* (32000 – 12000)/12000

= 100 * 20000/12000

= 166.67%

This measurement of return is the simplest and it does not consider time period. Most times it produces a large number so people are impressed!

Average Annual Return (AAR)

Average annual return (AAR) is the arithmetic mean of a series of rates of return. The formula for AAR is:

AAR = (Return in Period 1 + Return in Period 2 + Return in Period 3 + …Return in Period N) / Number of Periods or N

Let’s look at an example. Assume that an investment XYZ records the following annual returns:

Year Annual Return

2005 20%

2006 25%

2007 22%

2008 -10%

AAR for the period from 2005 to 2008: = (20% + 25% + 22% -10%) / 4 = 57%/4 = 14.25%

AAR is somewhat useful for determining trends . AAR is typically not regarded as a correct form of return measurement and thus it is not a common formula for analysis.

Compound Annual Growth Rate or CAGR

CAGR is the year-over-year growth rate of an investment over a specified period of time. It’s an imaginary number that describes the rate at which an investment would have grown if it grew at a steady rate.

Let’s assume you invested Rs 10,000 in Apr 2010 and by Apr 2011 your investment became Rs 30,000, by Apr 2012 it became Rs 15,000. What was the return on your investment for the period?

The formula to calculate CAGR is :

CAGR Formula

So CAGR for above example is :

= ((15,000/10,000) ^ (1/2)) -1

= 22.47%

If the investment states that it had an 8% annualized return over ten years, that means if you invested on Apr 1, and sold your investment on Mar 31 exactly ten years later, you earned the equivalent of 8% a year. However, during those ten years, one year the investment may have gone up 20% and another year it may have gone down 10%. In the example if the investment Rs 10,000 would have grown at the rate of 22.47% every year and at end of two years it would be Rs 15,000 as shown in calculation below.

Year Initial Value Growth Final Value

1 10,000 2,247 12,247

2 12,247 2752 15,000.

FUND RISK AND RETURN

Birla sun life medium term fund – growth

Mean - 9.86% Standard Deviation - 1.92% Beta - 0.31 Absolute Return from date 26-3-2008 to 22-01-2014 is 49.4 %* * Returns have been calculated after adjusting the NAVs for dividends, & bonus, if any. CAGR – 10.46% HDFC medium term opportunities – growth

Mean - 8.66% Standard Deviation - 2.48% Beta - 0.46 Absolute Return from date 29-10-2010 to 22-01-2014 is 34.7%* * Returns have been calculated after adjusting the NAVs for dividends, & bonus, if any. CAGR – 7.4% Franklin India Blue chip - Growth

Mean - 3.83% Standard Deviation - 16.42% Beta - 0.85 Absolute Return from date 01-01-1999 to 22-01-2014 is 2555.1 %* * Returns have been calculated after adjusting the NAVs for dividends, & bonus, if any. NAV on 01-01-1999 is 9.27 & NAV on 22-01-2014 is 246.12860. CAGR - 1%.

ICICI Prudential Focused Bluechip Equity Growth

Mean - 6.55% Standard Deviation - 16.79% Beta - 0.88 Absolute Return from date 26-05-2008 to 22-01-2014 is 103.0 %* * Returns have been calculated after adjusting the NAVs for dividends, & bonus, if any. NAV as on date 26-05-2008 is 10.00 & on 22-01-2014 is 20.3400 CAGR – 7.13%

THANK YOU