risk return calculation

8/12/2019 Risk Return Calculation

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Risk and Return (Theory)

1) Risk and return fundamentals2) Risk aversion utility CML and CAL

Risk and return fundamentals

Investment Alternative use of saving or Rational use of saving or Best use of saving or

sacrifice of person resources for sometimes

Planning for future consumption Purchase of real or financial assets

Why investment?

To get additional financial benefit (capital gain and normal gain) To save the money from inflation To consume in future To maintain liquidity Excitement of interests To increase wealth position

Main concerns of investments

RResources sacrifice today certain RReturn expectation future uncertain RRisk involvement function during the period TTime time holding period duration EEnvironment factors and influencesfavorable and unfavorable

Return analysis

Return reward of investment

Increment in value of wealth Additional financial benefit Cost of compensation paid for bearing risk and waiting time.

Risk and Return

Portfolio

Analysis

(Chapter - 4)

Assets pricing

model

(Chaper - 5)


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Sources of return

Return comes from two sources

1. Capital gainincrement in price2. Normal gainregular cash flow i.e interest and dividend

Measurement of returnRealized rate of return (past) and expected rate of return (future) are the two forms of

return which are measured as under.

1. Holding period return (HPR)Example

Date Price Dividend

1-1-2011 8000 -

31-12-2011 8100 500

31-12-2012 11000 100

31-12-2013 - -

Find the HPR of Mr. A of his investment

Stock NSO Po P1 D1 HPR

A 10 100 115 5 20%

B 20 200 220 10 15%


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AM and GM return

For exampleI

Year 1 2 3 4 5Rj 6% 7 9 10 8

GM is the annualized return between FV and PV i.e with compounding concept

Conclusion of AM and GM

If there is no fluctuation in periodic returns then AM=GM If there is fluctuation in periodic returns then GMAM GM uses actual compounding effect but AM is biased GM is better for decision

Effective rate of return Real rate of return

That inflation adjusted actual rate of return which expresses the additional purchasing

power of investor.

where, q = inflation rateExpected rate of return

Forecasted rate of return by using future date and respective probabilities is known as

expected rate of return.

Where,


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For example

State Rj Pj Rj*Pj

V bad 8 0.1 0.8Bad 10 0.2 2

Average 12 0.4 4.8

Good 14 0.2 2.8

V good 16 0.1 1.6

12%

For equal probability case

Or, Required rate of return (RRR) = cost = Rf+ (RmRf) i

Risk

Uncertainties on future results or outcomes are known as risk. Fluctuation or variation or deviation in rate of return is known as risk. Higher the variation, higher the risk, lower the variation, lower the risk and if there

is no variation there is no risk.

For example:

Year Rj Rp Rt 1 -2 8 10 144 4

2 22 9 10 144 1

3 -10 10 10 400 0

4 32 11 10 484 1

5 8 12 10 4 4

Rj= 50 Rp= 50 Rt= 50

High risk high

variation

Low risk

low variation

No risk no

variation

Standard deviation


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Standard average volatility throughout the period. Standard dispersion around the mean.

Variance = square of S.D

Co-variance between two assets

It is a statistical tool which is used to

-

Show the relationship between two stocks return whether positive ornegative.

- To show whether they are moving in same direction or opposite direction.Correlation coefficient

Covariance only shows positive or negative relationship but is silent about the degree of

relationship. So to find degree of relationship we calculate coefficient between A and B.

rAB= AB = covAB/AB

Portfolio

What?Combination of more than one asset in investment.

Why?To minimize the risk for stable return

How?Possible loss from one will be covered by gain of others.

Who?Harry M. Markowitz

When? - 1952What assumption? - Not put all eggs in a single basket.

Expected return of portfolio

It is simply the weighted average of return of individual assets which are included in

portfolio. The expected return of portfolio depends upon following two factors.


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risk return calculation

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