Risk & return cf presentaion

 The primary financial goal is shareholder wealth
maximization, which translates to maximizing stock
price.
 Maximize stock value by:
◦ Forecasting and planning
◦ Investment and financing decisions
◦ Coordination and control
◦ Transactions in the financial markets
◦ Managing risk
1

 It is the reward for undertaking the investment
The Two Components of Return
1. Yield: The income component of a security’s return
2. Capital gain (loss): The change in price on a
security over some period of time
Putting The Two Components Together
Total return = Yield + Price change
Where: the yield components can be 0 or +
the price change components can be 0, +, or -
2

 “Risk comes from not knowing what you are doing”
Warren Buffet
 The chance that the actual outcome from an
investment will differ from the expected outcome.
 Future returns from an investment are unpredictable
 Risk = Probability of occurrence * Impact on objects
3

 Market Risk
 Business Risk
 Liquidity Risk
 Exchange Rate Risk or Currency Risk
 Country Risk
 Execution Risk
 Interest Rate Risk
 Re-Investment Risk
 Inflation Risk
4

Total Return (TR)
Percentage measure relating all cash flows on a
security for a given time period to its purchase price
TR= Any cash payment received + Price change over the period
Price at which the asset is purchased
How to Calculate Total Return
TR= CFt +(PE - PB) = CFt +PC
PB PB
6

Example: 100 shares of data shield are purchased at
$30 per share and sold one year later at $35 per
share. A dividend of $2 per share is paid.
Stock TR = 2+(35-30)/30
= 2+(5)/30
= 0.2333 or 23.33%
7

Example: Assume the purchase of a 10% coupon
Treasury bond at a price of $960, held 1 year, and
sold for $1020. The TR is
Bond TR = 100+(1020-960)/960
= 100+60/960
= 0.1667 or 16.67%
8

Year S&P 500 TRs (%)
1990 -3.14
1991 30.00
1992 7.43
1993 9.94
1994 1.29
1995 37.11
1996 22.68
1997 33.10
1998 28.34
1999 20.88
9
Source: Jones, Charles P, Investment; P. 148; 10th ed. ; National Book
Foundation 2010

Arithmetic Mean = X = x/ n
= [-3.14+30+…+20.88]/10
= 187.63/10
= 18.76
Geometric Mean=G=[(1+TR1)(1+TR2)…(1+TRn)]1/n - 1
=[(.9687)(1.30001)(1.07432)(1.09942)(1.01286)(1.37113)
(1.22683)(1.33101)(1.28338)(1.2088)]1/10 - 1
=1.18-1
=0.18 or 18%
10
S

Cumulative Wealth Index
- Cumulative wealth over time given an initial wealth
and a series of returns on some assets
CWIn = WI0 (1+TR1)(1+TR2)…(1+TRn)
Where
CWIn = the cumulative wealth index as of the end of period n
WI0 = the beginning index value, typically $1
TR1,n = the periodic TRs in decimal form
CWI90-99 =1.00(.9687)(1.30001)(1.07432)(1.09942)(1.01286)
(1.37113)(1.22683)(1.33101)(1.28338)(1.2088)
= 5.2342
11

12
 The future is uncertain.
 Investors do not know with certainty whether the
economy will be growing rapidly or be in recession.
 Investors do not know what rate of return their
investments will yield.
 Therefore, they base their decisions on their
expectations concerning the future.
 The expected rate of return on a stock represents
the mean of a probability distribution of possible
future returns on the stock.

13
 Given a probability distribution of returns, the
expected return can be calculated using the
following equation:
N
E[R] = S (piRi)
i=1
 Where:
◦ E[R] = the expected return on the stock
◦ N = the number of states
◦ pi = the probability of state i
◦ Ri = the return on the stock in state i.

14
 Risk reflects the chance that the actual return on an
investment may be different than the expected
return.
 One way to measure risk is to calculate the variance
and standard deviation of the distribution of
returns.
Var(R) = s2 = S pi(Ri – E[R])2
i=1
 Where:
◦ Ri = the return on the stock in state i
◦ E[R] = the expected return on the stock


15
 The standard deviation is calculated as the positive
square root of the variance:
SD(R) = s = s2 = (s2)1/2 = (s2)0.5

The ratio of the standard deviation of a
distribution to the mean of that distribution.
It is a measure of RELATIVE risk.
CV =s/E(R)

17
 Probability Distribution:
State Probability Return On Return On
Stock X Stock Y
1 20% 5% 50%
2 30% 10% 30%
3 30% 15% 10%
4 20% 20% -10%

18
State of
Economy Prob. Return X
Pi X (in %) Pi*Ri (Ri – E[R]) (Ri – E[R])2 pi(Ri – E[R])2
1 0.25.00 1.00(7.50) 56.25 11.25
2 0.310.00 3.00(2.50) 6.25 1.875
3 0.315.00 4.502.50 6.25 1.875
4 0.220.00 4.007.50 56.25 11.25
SUM 12.5 26.25
E[R] 12.50 Variance 26.25
SD 5.12
CV 0.41

19
State of
Economy Prob. Return
Pi Y (in %) Pi*Ri (Ri – E[R]) (Ri – E[R])2 pi(Ri – E[R])2
1 0.250.00 10.0037.50 1,406.25 281.25
2 0.330.00 9.0017.50 306.25 91.88
3 0.310.00 3.00(2.50) 6.25 1.88
4 0.2(10.00) -2.00(22.50) 506.25 101.25
SUM 20.00 476.25
E[R] 20.00 Variance 476.25
SD 21.82
CV 1.09

20
 The variance and standard deviation for stock X is calculated as
follows:
 E[R]X = .2(5%) + .3(10%) + .3(15%) + .2(20%) = 12.5%
s2
X = .2(.05 -.125)2 + .3(.1 -.125)2 + .3(.15 -.125)2 + .2(.2 -.125)2
= .002625
sX = (.002625)0.5 = .0512 = 5.12%
CV = 5.12/12.5 = 0.41

21
E[R]Y = .2(50%) + .3(30%) + .3(10%) + .2(-10%) =20 %
s2
y = .2(.50 -.20)2 + .3(.30 -.20)2 + .3(.10 -.20)2 + .2(-.10 -
.20)2 = .042
sy = (.042)0.5 = .2049 = 20.49%
CV = 20.49 / 20 = 1.09
 Although Stock Y offers a higher expected return than Stock X, it
is also riskier since its variance and standard deviation are greater
than Stock X's.

Certainty Equivalent (CE) is the amount of cash
someone would require with certainty at a point
in time to make the individual indifferent
between that certain amount and an amount
expected to be received with risk at the same
point in time.

Certainty equivalent > Expected value
Risk Preference
Certainty equivalent = Expected value
Risk Indifference
Certainty equivalent < Expected value
Risk Aversion
Most individuals are Risk Averse.

You have the choice between (1) a
guaranteed dollar reward or (2) a coin-flip
gamble of $100,000 (50% chance) or $0
(50% chance). The expected value of the
gamble is $50,000.
•Mary requires a guaranteed $25,000, or more, to
call off the gamble.
•Raleigh is just as happy to take $50,000 or take
the risky gamble.
•Shannon requires at least $52,000 to call off the
gamble.
Risk Attitude Example

What are the Risk Attitude tendencies of each?
Mary shows “risk aversion” because her
“certainty equivalent” < the expected value of
the gamble.
Raleigh exhibits “risk indifference” because her
“certainty equivalent” equals the expected value
of the gamble.
Shannon reveals a “risk preference” because her
“certainty equivalent” > the expected value of
the gamble.

 Weak Form ME:
◦ fully reflect all currently available security market
data about price and volume.
 Semi Strong ME:
◦ fully reflect all publically available information
 Strong Form ME;
◦ fully reflect all information from both public and
private
8-
26

27
 The Expected Return on a Portfolio is the weighted average of the
expected returns on the stocks which comprise the portfolio.
 This can be expressed as follows:
N
E[Rp] = S wiE[Ri]
i=1
 Where:
◦ E[Rp] = the expected return on the portfolio
◦ N = the number of stocks in the portfolio
◦ wi = the proportion of the portfolio invested in stock i
◦ E[Ri] = the expected return on stock i

28
 The variance/standard deviation of a portfolio reflects not only the
variance/standard deviation of the stocks that make up the portfolio but also how
the returns on the stocks which comprise the portfolio vary together.
◦ Covariance is a measure that combines the variance of a stock’s returns with
the tendency of those returns to move up or down at the same time other
stocks move up or down.
◦ Correlation coefficient, is often used to measure the degree of co-movement
between two variables. The correlation coefficient simply standardizes the
covariance.
◦ Its range is from –1.0 (perfect negative correlation), through 0 (no
correlation), to +1.0 (perfect positive correlation).

29
 The Covariance between the returns on two stocks can be
calculated as follows:
N
Cov(RX,RY) = sX,Y = S pi(RXi - E[RX])(RYi - E[RY])
i=1
 Where:
◦ sX,Y = the covariance between the returns on stocks X and Y
◦ RXi = the return on stock X in state i
◦ E[RX] = the expected return on stock X
◦ RYi = the return on stock Y in state i
◦ E[RY] = the expected return on stock Y

30
 The Correlation Coefficient between the returns on two stocks can
be calculated as follows:
sX,Y
Corr(RX,RY) = rX,Y = sX sy
 Where:
◦ rX,Y =the correlation coefficient between the returns on stocks X
and Y
◦ sX,Y =the covariance between the returns on stocks X and Y,
◦ sX =the standard deviation on stock X, and
◦ sy =the standard deviation on stock Y

31
 The covariance between stock X and stock Y is as
follows:
sX,Y = .2(.05-.125)(.5-.2) + .3(.1-.125)(.3-.2) +
.3(.15-.125)(.1-.2) +.2(.2-.125)(-.1-.2) = -.0105
 The correlation coefficient between stock X and stock
Y is as follows:
-.0105
rX,Y = (.0512)(.2049) = -1.00

32
 Most investors do not hold stocks in isolation.
 Instead, they choose to hold a portfolio of several stocks.
 When this is the case, a portion of an individual stock's risk
can be eliminated, i.e., diversified away.
 From our previous calculations, we know that:
◦ the expected return on Stock X is 12.5%
◦ the expected return on Stock Y is 20%
◦ the variance on Stock X is .00263
◦ the variance on Stock Y is .04200
◦ the standard deviation on Stock X is 5.12%
◦ the standard deviation on Stock Y is 20.49%

33
 Using either the correlation coefficient or the
covariance, the Variance on a Two-Asset Portfolio can
be calculated as follows:
s2
p = (wA)2s2
x + (wy)2s2
y + 2wxwy rX,Y sxsy
OR
s2
p = (wA)2s2
x + (wy)2s2
y + 2wxwy sx,y
 The Standard Deviation of the Portfolio equals the
positive square root of the variance.

34
 Expected Return, Variance and standard deviation of a
Two Asset portfolio:
Investment Proportions: 75% stock X and 25% stock Y:
 E[Rp] = 0.75 (0.125) +0.25(0.20) =0.14375 or 14.375%
s2
p =(.75)2(.0512)2+(.25)2(.2049)2+2(.75)(.25)(-1)(.0512)(.2049)
= .00026
sp = .00016 = .0128 = 1.28%

Summary of the Portfolio Return and
Risk Calculation
X Y Portfolio
Weights 0.75 0.25
E [R] 12.50 20.00 14.375
Variance 26.25 476.25 2.60
SD 5.12 21.82 1.613
CV 0.4099 1.0912 0.1122
Corr (x,y) -1.00

8-
36
Corr
(x,y)
Weights
(x,y) E [R] Variance SD
1 0.75,0.25 14.38 86.46 9.30
0.75 0.75,0.25 14.38 75.98 8.72
-1.00 0.75,0.25 14.38 2.60 1.61
0.5 0.75,0.25 14.38 65.50 8.09
0.25 0.75,0.25 14.38 55.01 7.42
0 0.75,0.25 14.38 44.53 6.67
-0.75 0.75,0.25 14.38 13.08 3.62
-0.5 0.75,0.25 14.38 23.57 4.85
-0.25 0.75,0.25 14.38 34.05 5.84
-1 0.75,0.25 14.38 2.60 1.61

INVESTMENT
RETURN
TIME TIME
TIME
SECURITY X SECURITY Y
Combination
X and Y
Diversification and the Correlation
Coefficient

 RF asset has zero SD and zero correlation of
returns with risky Portfolio
 SD of Portfolio = (Wa) (SDa)
8-
38

 While diversification of portfolio, there are
two kinds of risk we will deal with:
- Unsystematic Risk
- Systematic Risk
- So,
Total Risk = Unsystematic Risk + Systematic
Risk

 An unsystematic risk, also called diversifiable,
unique, firm specific risk, is one that is particular
to a single asset or, at most, a small group.
For example, if the asset under consideration is
stock in a single company,
- The positive NPV projects( successful new
products, cost saving) will tend to increase the
value of stock.
- Unanticipated lawsuits, industrial accidents,
strikes etc will decrease the FCF’s and thereby
decrease the share values.

 Unsystematic risk is essentially eliminated by
diversification, so a portfolio with many
assets has almost no unsystematic risk.

 Systematic risk, also called as undiversifiable,
unavoidable, market risk, is due to factors that
affect overall market, such as,
- Changes in nation’s economy
- Tax reforms
- Change is world energy situation
 These are the risks that affect securities overall(
whether in a portfolio or single) and,
consequently, cannot be diversified away.
 An investor who holds a well-diversified portfolio
will be exposed to this type of risk.

Total
Risk
Unsystematic risk
Systematic risk
STD
DEV
OF
PORTFOLIO
RETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Total Risk = Systematic Risk + Unsystematic Risk

 The systematic risk principle states that the
reward for bearing risk depends only on the
systematic risk of an investment.
- The underlying rationale for this principle is
straight forward: because unsystematic risk
can be eliminated at virtually no cost(by
diversifying), there’s no reward for bearing it.
- No matter how much total risk an asset has,
only the systematic risk is relevant
determining the expected return and risk
premium on that asset.

 Beta is an index of systematic risk.
 Beta (β) of a stock or portfolio is a number
describing the relation of its returns with those
of the market as a whole.
 The sensitivity of an asset’s return on the market
index.
 A measure of the volatility, or systematic risk, of
a security or a portfolio in comparison to the
market as a whole.
 Beta is a standardized measure of the covariance
of the asset’s return with the market return.
45

 Beta = Covariance of Asset’s return with
market return / variance of market return
= Cov im/ s2
m
 The beta of a portfolio is simply a weighted
average of the individual stock betas in the
portfolio.

47
bp = Weighted average
= 0.5(bX) + 0.5(bY)
= 0.5(1.29) + 0.5(-0.86)
= 0.22

 The typical analysis involves either monthly or weekly returns
on the stocks and on the market index for 3-5 years.
 Many analysts use the S&P 500 to find the market return.
 Analysts typically use four or five years’ of monthly returns to
establish the regression line like Merill Lynch.
 Some analysts use 52 weeks of weekly returns like Value
Line.
 Go to http://finance.yahoo.com
Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell,
then click GO.
48

•Obtaining Betas
• Can use historical data if past best represents
the expectations of the future.
•Adjusted Beta
• There appears to be a tendency for the
measured betas of individual securities to
revert eventually toward the beta of the market
portfolio.
• This might be due to the economic factors
affecting the operations and financing of the
firm.

 A line that describes the relationship between an individual
security’s returns and returns on the market portfolio.
 It is useful to deal with returns in excess of the risk free rate.
 The excess return is simply the expected return less the risk
free return.
 There are two ways of determining the relationship b/w
excess return on stock and market portfolio.
- Historical data (with the assumption that relationship will
continue in future)
- Security Analysts.

EXCESS RETURN
ON STOCK
EXCESS RETURN
ON MARKET PORTFOLIO
Beta =
Rise
Run
Unsystematic Risk
Characteristic Line
Characteristic Line

 Greater the slope, greater the systematic risk.
 Alpha is intercept of characteristic line on vertical
axis.
 If excess returns for market portfolio were zero,
alpha would be the expected excess return for
the stock.
 Beta is slope of characteristic Line = Rise/Run
i.e. Change in Stock’s Return/ Change in Market
Return
 The monthly returns are calculated as:
(Div paid) + (Ending price – beginning price)/
Beginning price

EXCESS RETURN
ON STOCK
EXCESS RETURN
ON MARKET PORTFOLIO
Beta < 1
(defensive)
Beta = 1
Beta > 1
(aggressive)
Each characteristic
line has a
different slope.
Characteristic Lines and Different Betas

 Aggressive Investment: A slope steeper than
1 means that the stock’s excess return varies
more than proportionally with the excess
return of market portfolio, it has more
systematic risk than market.
 Defensive Investment: A slope less than 1
means that the stock’s excess returns varies
less than proportionally with the excess
return of the market portfolio. It has less
systematic risk than market.

 If b = 1.0, stock has average risk.
 If b > 1.0, stock is riskier than average.
 If b < 1.0, stock is less risky than average.
 Most stocks have betas in the range of 0.5 to 1.5.
 A positive beta means that the asset's returns generally follow
the market's returns, in the sense that they both tend to be
above their respective averages together, or both tend to be
below their respective averages together.
 A negative beta means that the asset's returns generally move
opposite the market's returns: one will tend to be above its
average when the other is below its average
55

 The CAP model was introduced by Jack Treynor, John
Lintner, William Sharpe and Jan Mossin in the early
1960’s.
 According to CAP model the investor needs to be
compensated in two ways, for time value of money
(risk free rate) and for taking systematic risk.
 In a competitive market, the expected risk premium
varies in direct proportion to beta.
 This model states the linear relationship between risk
(systematic) and expected (required) return.
 A security’s expected return is risk free rate plus a
premium based on the systematic risk of security.
 Rj = Rf + bj(RM – Rf)

 Capital markets are efficient.
 Homogeneous investor expectations over a given period.
 Investors all think in terms of a single holding period.
 There are no taxes and no transactions costs.
 All investors are price takers, that is, investors buying and
selling won’t influence stock prices.
 Quantities of all assets are given and fixed.
 Risk-free asset return is certain.
 Market portfolio contains only systematic risk (use S&P
500 Index or similar as a proxy).
 Investors can borrow or lend unlimited amounts at the
risk-free rate.

 The least risky investment is T-bills, since the
return on them is fixed, it is unaffected by
what happens to the market. (beta = 0),
 The riskier investment is market portfolio of
common stocks (average beta = 1)
 Risk premium(excess return) is expected
returns minus risk free return.
 The relationship between systematic risk and
expected return in financial markets is
usually called the security market line (SML).

 The relationship between an individual security’s expected
rate of return and it’s systematic risk as measured by beta
will be linear, this relationship is called as Security Market
Line.
Rf
RM
Required
Return
Risk
Premium
Risk-free
Return
bM = 1.0
Systematic Risk (Beta)

 Now, if everyone holds the market portfolio,
and if beta measures each security’s
contribution to the market portfolio risk, then
it’s no surprise that the risk premium
demanded by investors is proportional to
beta.
 This is what the CAPM says!

Systematic Risk (Beta)
Rf
Required
Return
Direction of
Movement
Direction of
Movement
Stock Y (Overpriced)
Stock X (Underpriced)
What if a stock does not lie on SML?

 Investors require some extra return for taking
risk, that is why common stocks are given
higher returns on average than t-bills.
 Investors are not concerned with those risks
that they cannot diversify, hence the
systematic risk the relevant risk only.

 Maturity of Risk free Security :
CAPM is one period model and investors are
concerned about the long term capital
investment returns.
 Faulty use of the market index
 CAPM/SML concepts are based on
expectations, yet betas are calculated using
historical data. A company’s historical data
may not reflect investors’ expectations about
future riskiness.

Risk & return cf presentaion

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