1. 3. Risk & Return
• Risk and return concepts & measures
• Relating returns and risks
• Time value of money

2. Return Concepts
• Return concepts
1. Actual return (historical return, realised return, ex post facto
return)
2. Expected return (ex ante, predicted, probability-based)
3. Required return (compensation for time & risk)
• In theory
– Expected return is equal to required return, if security price is
equal to its fair value
– If expected returns is not equal to required return, security is
mispriced
• Investment decision
– ‘Buy’ a security if expected return > required return*
– A security was a good investment if actual return was greater
than or equal to the required return
* greater than sign is due to a ‘margin of safety’ (relevant for future but not for past)

3. Risk Concepts
• Sources of total risk
– Market risk vs company-specific (unique) risk
– Systematic risk vs unsystematic risk
• In theory
– Unsystematic risks are diversifiable and there is no
compensation for these risks.
• Risk measures
– Historical risk (ex post facto)
– Predicted risk (ex ante, probability-based)

4. Systematic & Unsystematic risks
• Systematic risks may be attributable to
fluctuations in macro-economic factors like
economic growth, government spending,
money supply, interest rates, inflation, etc.
• Unsystematic risks usually arise from
company-specific factors such as product
failure, competition, production constraints
etc. Unsystematic risks are diversifiable.

5. Measures for Return
• Measures for realised return
– Holding period return: total return, annualised return
– Return relative and cumulative wealth index
– Average return over multiple periods (statistical measure)
• Arithmetic mean
• Geometric mean (time-weighted return)
– Real world impact: inflation, taxes & exchange rates
• Inflation: real vs nominal return
• Taxes on income/dividends and capital gains
• Impact of exchange rates for international investments
• Estimation of expected return
– Expected holding period return based on a target price, or
– Expected return based on probability distribution of returns

6. Holding Period Return
• Holding period return
HPR = [(P1-P0) + C]/P0
where P0 is price at the beginning of the holding period (or
purchase price),
P1 is price at the end of the holding period,
C is the cashflow to the investor during the period (dividend
paid on shares/ interest paid on bonds)
Restating the formula, P0 = (P1 + C)/(1+R); (P1 + C) = P0 (1+R)
• Annualised return
If r denotes annual return and t denotes holding period in years
(1+HPR) = (1+r)t
HPR = (1+r)t - 1
r = (1+HPR)1/t - 1
• Real return = (1+Nominal return)/(1+Inflation) - 1

7. Statistical measures for Risk
• Historical risk
– Based upon variability of returns
• Variance & standard deviation (volatility)
• Criticism of above measures
– Do not differentiate ‘down-side risk’ : semi-variance
– Ignore shape of probability distribution: Skewness and
kurtosis
• Predicted risk
– Based on variability of expected returns

8. Measures of Security Return and Risk
Historical (Ex post
facto)
Expected (Ex ante)
Mean Return 𝑟 = Σri/n E(r) = Σpi ri
Variance (σ2) and
Standard Deviation
(σ)
σ2 = Σ(ri – 𝑟)2/(n-1) σ2 = Σpi(ri – E(ri))2
1. 𝑟 is mean historical return & σ the standard deviation of ri, &
ri denotes return for period i, where i = 1,2….n.
2. E(r) is expected return & σ is the standard deviation of
expected ri, & i =1,2.. denote mutually exclusive states with
expected return ri and probability pi

9. Relating Return & Risk
• Suppose that an investor is provided two investment alternatives as shown above.
The two alternatives have the same expected return.
– However, a risk averse investor would prefer the risk-free alternative in this case.
For the same level of expected return, the risk-free alternative is more valuable.
– In fact, the risk averse investor may be ready to accept lower expected return, till a
point where the investor is indifferent between an alternative which provides a
lower but certain expected return, and an alternative which provides a higher but
uncertain expected return. The former is known as the certainty equivalent value
of the latter.
– Hence required return for risky investment > required return for a risk free
certainty equivalent investment
– The difference in required returns between a risky investment and its certainty
equivalent risk-free investment is known as risk premium.
Risk-free alternative Risky alternative
P0 Rs 40,000 Rs 40,000
P1 Rs 50,000 (p=100%) Rs 100,000 (p=50%),
Rs 0 (p=50%)
E (P1) Rs 50,000 Rs 50,000
E (ri) 25% 25%
σ 0 125%

10. Investor’s Risk Preference: Indifference Curves
Highly
Risk
Averse
Moderat
ely Risk
Averse
Less Risk
Averse
Risk
Neutral
Risk
Seeker
Speculator
Gambler
ExpectedReturn
Standard Deviation
The total satisfaction derived by an investor from a given return and risk trade-off is the ‘utility’ of that
investor for that combination. Investors may derive the same utility from different combinations of
return and risk. A curve joining all the return and risk combinations for which the utility to the investor
is the same is known as an indifference curve.
The risk aversion of an investor determines the slope of an indifference curve, while the level of utility
determines its position. In the first graph, investor A is more risk averse than investor B. For A, curve
A1 represents higher utility than curve A2, because every point on A1 provides more return for the
same level of risk than A1. Similarly curve B1 represents higher utility than B2.
ExpectedReturn
Standard Deviation
A1
A2 B1
B2

11. Measuring relationship between
Return and Risk
• The models quantifying the relationship between
required return and risk are called return
generating models or return models (also known
as asset pricing theories)
• The most common models/theories* are
– The market model
– The capital asset pricing model
– The arbitrage pricing theory
– The multifactor models
*These will be discussed in subsequent sessions

12. Time value of Money
• Relationship between Future Value (FV) &
Present Value (PV) of money
– FV = PV (1+r)n
• The power of compounding means that small
differences in rates of return can result in
significant changes in cumulative wealth
• Calculating FV & PV
– of one-time cashflow (formula above)
– of uneven cash flows
– of annuity
– of perpetuity

13. Time Value Calculations*
• Uneven Cash Flows: C1, C2….Cn
– PV = ΣCt/(1+r)t
– FV = PV(1+r)n
• Annuity: Cash Flow C x n periods
– PV = C [(1-(1/(1+r)n)/r]
– FV = C [(1+r)n-1]/r
• Perpetuity: Cash Flow C
– PV = C/r
• Growing Perpetuity: Cashflow C, Growth rate g
– PV = C/(r-g)
*Will be relevant during the sessions on Valuation

14. Relationship between Security Price
and Returns
• Present value of an investment is inversely
related to the required return
– PV = ΣCi/(1+r)i ; C1…Cn are inflows, r is required return
• According to valuation theories, fair price of a
security is equal to the PV of future inflows
• Assuming no mispricing, security price = fair price
(PV); and expected returns = required returns
• Hence security price is inversely related to return
• Ex. bond prices fall, when interest rates rise

15. Relationship between Stock Returns
and Return on Equity
1. Return on equity (RoE or Return on Networth) is an accounting concept,
based upon historical value of equity and not on market stock prices
2. Hence RoE is not the same as stock return, which is based on the market
price paid by the stock owner
3. According to valuation models, fair value of a stock is related to its RoE.
4. But since RoE does not impact risks, it is not related to required returns.
5. If stocks are not mispriced, expected returns are equal to required
returns. Hence, expected returns should not be related to RoE.
6. Statements 3 & 5 are not contradictory. If fundamentals of a company
increase (as reflected for ex. by an increase in RoE), its stock prices will
also increase such that the expected return tends to become equal to the
required return.
7. Conversely, if fundamentals of a company worsen, resulting in lower
expected cash flows and RoE, its stock prices will decline such that the
expected stock return tends to become equal to the required return.
Not for syllabus

16. Building blocks of Security Analysis
• Risk-return concepts: How to calculate historical and
expected returns and risks?
• Time value of money: Relationship between present value
and future cash flows
• Portfolio theory: How is return related to risk in a portfolio
context
• CAPM (& other return models): How to calculate required
return based on risk?
• EIC analysis: How to project future cash flows of a firm?
• Valuation theory: How to estimate fair value of a security
based on future cash flows or dividends (projected based
on EIC) and required returns (estimated based on a return
model)?
• Efficient market hypothesis: Whether security analysis is a
value-adding activity?

17. Reading references & Home work
• Reading Ref: PC Ch 4, BKMM Ch 5 & 6
– IBS Case Study: Comparing Sensex returns & Fixed deposits
• Home Work
– For your assigned company:
• Take monthly stock prices for 5 years (60 data points) from BSE/NSE
websites and BSE 30 index/Nifty 50
• Adjust the prices for any bonus/splits/consolidations
• Calculate the monthly returns from the monthly price series for the
stock and for the index
• Calculate arithmetic and geometric mean returns for the stock and for
the index
• Calculate the variance and standard deviation for the stock and for the
index
• Comment upon the average return and risk for your stock compared
with the index