Topic 4

Risk and Return

 Learning Objectives

 To define risk and return.

 To discuss the investors behavior towards risk.
 To calculate the expected rate to return of a security.
 To elucidate the measurement of risk in investments using standard
deviation and coefficient of variation.
 To discuss the diversification concept as a method in risk reduction.
 To explain the characteristic line and beta in measuring the systematic
risk.
 To calculate the required rate of return and beta of a portfolio.
 To discuss the importance and the used of Capital Asset Pricing Model
(CAPM).
 To discuss the effects of inflation on rate of return.
 Return
Return represents the total gain or loss on an investment.

You invested in 1 share of Apple (AAPL) for $95 and sold a year later
for $200. The company did not pay any dividend during that period.
What will be the cash return on this investment?

Cash Return = $200 + 0 - $95 = $105

Rate of Return = ($200 + 0 - $95) ÷ 95 = 110.53%

Expected return is what you expect to earn from an investment in the
future.

It is estimated as the average of the possible returns, where each

possible return is weighted by the probability that it occurs.

Where:
Pb1 = probability of occurrence of the outcome
r = return for the outcome
n = number of outcomes considered

Expected Return (k^ ) the return that an investor expects to earn on an asset,
given its price, growth potential, etc.

‡Required Return ( k- ) the return that an investor requires on an asset given its
risk and market interest rates.
 Risk
• Risk is defined as the chance of suffering a financial loss. Or the
potential variability in future cash flows.

• Risk may be used interchangeably with the term uncertainty to

refer to the variability of returns (possible outcomes).

•The wider the range of possible future events that can occur, the
greater the risk.

• Potential variability in future cash flow refers to the possibility that

an actual return will differ from our expected return.

• A greater chance of loss is considered riskier than those with a

lower chance of loss.
Relationship between risk and return
 Measurement Risk
• Standard deviation (S.D.) is one way to measure risk. It measures the
volatility or riskiness of returns. ( -sigma)

• S.D. = square root of the weighted average squared deviation of each

possible return from the expected return.

This variability in returns can be quantified by computing the Variance

or Standard Deviation in investment returns.

the standard deviation, k, which measures the dispersion around the
expected value.
State of Probability Return
Economy (P)
Company A Company B
Recession 0.20 4% -10%
Normal 0.50 10% 14%
Boom 0.30 14% 30%

k (A) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

k (B) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

Based only on your expected return calculations, which

stock would you prefer?

Have you considered risk??????????

 Example
Company A Company B
( 4% - 10%)2 (.2) = 7.2 (-10% - 14%)2 (.2) = 115.2
(10% - 10%)2 (.5) = 0 (14% - 14%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8 (30% - 14%)2 (.3) = 76.8
Variance = 12 Variance = 192
Stand. dev. = 12 = 3.46% Stand. dev. = 192 = 13.86%

Company A company B
Expected Return 10% 14%
Standard Deviation 3.46% 13.86%

Which company is good. It depends on your tolerance for risk!

We can conclude that, company A has lower risk compared to

company B, BUT Company B has higher return.

Remember, there’s a tradeoff between risk and return.

The coefficient of variation, CV, is a measure of relative
dispersion that is useful in comparing risks of assets with differing
expected returns.

CV =  / k

The higher the CV, the higher the risk.

CV A = 3.46 % / 10%
= 0.346

CV B = 13.86% / 14%
= 0.99

A unit of risk in return for asset B is higher than asset A.

As a conclusion, asset A is less risky than asset B.

In comparing risk, it is more effective if we are using CV because it

considers the relative size or the rate of return.
 Portfolio and Diversification
• An investment portfolio is any collection or combination of financial
assets.

• If we assume all investors are rational and therefore risk averse, that
investor will ALWAYS choose to invest in portfolios rather than in single
assets.

•Investors will hold portfolios because he or she will diversify away a portion
of the risk that is inherent in “putting all your eggs in one basket.”

• If an investor holds a single asset, he or she will fully suffer the

consequences of poor performance.

• This is not the case for an investor who owns a diversified portfolio of
assets.
 Diversification
 Diversification: spreading out of investments to reduce risks.
 Investments across different securities rather than invest in
only one stock.
 Reducing a risk of portfolio depends on the correlation (r)
between all of the stocks.
 Correlation is a statistical measurement of the relationship
between two variables.
Positive Correlation
Negative Correlation
Possible correlations range from +1 to ʹ1
 Investment risks
 Investors should NOT expect to eliminate all risk from their portfolio. Some risk
can be diversified away and some cannot.
 Market risk (systematic risk) is nondiversifiable. This type of risk cannot be
diversified away. Such as Unexpected changes in interest rates. Unexpected
changes in cash flows due to tax rate changes, foreign competition, and the
overall business cycle.
 Company-unique risk (unsystematic risk) is diversifiable. This type of risk can
be reduced through diversification.
Such as A company’s labor force goes on strike.
A company’s top management dies in a plane crash.
A huge oil tank bursts and floods a company’s production area.
Investment risks
 Market portfolio
 Market portfolio is a portfolio consisting of a weighted sum
of every asset in the market, with weights in the proportions
that they exist in the market.
Proxy can be used as a market portfolio such as S&P 500
Index in the U.S and Nikkei 225 Index in Japan.
In Malaysia, Bursa Malaysia (formerly known as KLSE) is one
of the proxies that can be used as market portfolio.
The movement in these indexes act as a benchmark to the
movement of the market.
 Measuring market risk

 Systematic risk called non-diversifiable risk because it is beyond the control of

the investor and the firm.
Systematic risk reflects mainly macroeconomic shocks that affect aggregate
behavior of the economy.
Market risk measured by beta (β = 1)
 Once the asset return and market return obtained, a graph is prepared to see
the relationship between asset return and market return. Asset return and
market return are plot on Y-X-axis.
When all the returns are plotted, draw a line of best-fit through coordinate
point (0,0), which we call Characteristic line.
 Measuring return

Market returns and assets returns for certain period can be determined
by looking at the percentage of changes in index or price based on
the following equation:
kt = (Pt / Pt – 1) – 1
Asset Return & Market Return
Asset Market
Period Price Return Index Return
0 19.00 853.42
1 19.29 1.53% 869.10 1.84%
2 20.90 8.34% 900.67 3.63%
3 19.54 -6.51% 901.89 0.14%
4 21.50 10.03% 923.80 2.42%
 Measuring market risk
 The slope of the line (beta), represents the average movement of the
firm’s stock returns in response to a movement in the market’s return i.e
the average relationship between a stock’s return and market’s returns.
 Interpreting beta (B)
A firm that has a beta = 1 has average market risk. The stock is no
more or less volatile than the market.
A firm with a beta >1 is more volatile than the market.
A firm with a beta < 1 is less volatile than the market.
A firm with a beta=0 has no systematic risk.
 Market risk

 Beta is a measure of how an individual stock’s returns vary with

market returns.
 Beta measures of the sensitivity of an individual stock’s return to
changes in the market.
It indicates the average response of a stock’s return to the change in
the market as a whole.
Example:
β = 1.2 means any increase/decrease by 1% in market return will
cause an increase or decrease by 1.2% in asset return.
 Measuring portfolio beta

Portfolio beta indicates the percentage change on average of

the portfolio for every 1 percent change in the general
market.
The portfolio beta is a weighted average of the individual
asset's beta and assets has its own beta.

β portfolio= Σ wj*βj
Where wj = % invested in stock j
βj = Beta of stock j
 Required Rate of Return (CAPM)
 We know how to measure risk, using standard deviation for overall risk
and beta for market risk.
 We know how to reduce overall risk to only market risk through
diversification.
 We need to know how much extra return we should require for
accepting extra risk.

What is the Required Rate of Return?

The return on an investment required by an investor given market
interest rates and the investment’s risk.
The minimum rate of return necessary to attract an investor to
purchase or hold a security.
The required return for all assets is composed of two parts: the risk-free
rate which is usually estimated from the return on treasury bills and a risk
premium which is a function of both market conditions and the asset
itself.
 Required Rate of Return (CAPM)
 This linear relationship between risk and required return is known as the
Capital Asset Pricing Model (CAPM).

 CAPM equation equates the required rate of return on a stock to the risk-
free rate plus a risk premium for the systematic risk.

The equation indicates that investor’s minimum acceptable rate of return is

equal to the risk-free rate plus a risk premium for assuming risk.
 CAPM- SML
 The Security Market Line (SML) is a graphic representation of
the CAPM, where the line shows the appropriate required rate of
return for a given stock’s systematic risk.
 CAPM- SML

 Risk-Free Rate: This is the required rate of return or discount rate for
risk-less investments. Risk-free rate is typically measured by U.S. Treasury
bill rate.
 Risk Premium: Additional return we must expect to receive for assuming
risk. As the level of risk increases, we will demand additional expected
returns.
 The risk premium for a stock is composed of two parts: The Market Risk
Premium which is the return required for investing in any risky asset rather
than the risk-free rate and beta.
 Beta, a risk coefficient which measures the sensitivity of the particular
stock’s return to change in market conditions.
 CAPM

Example: ABC Corporation wishes to determine the required return on asset

Z, which has a beta of 1.5. The risk-free rate of return is 7%; the return on
the market portfolio of assets is 11%.
K Z = 7% + 1.5 [11% - 7%]
= 13% According to the CAPM, Asset Z should be priced to give a 13% return.
 REQUIRED RATE OF RETURN - CAPM
 Investor’s required rate of returns is the minimum rate of
return necessary to attract an investor to purchase or hold a
security.
 The required return for all assets is composed of two parts:
the risk-free rate and a risk premium.
The risk-free rate (Rf) is usually The risk premium is a function of
estimated from the return on both market conditions and the
treasury bills asset itself.
 SML – The line that reflect the attitude of investors
regarding the minimal acceptable return for a given level
Required of systematic risk.
rate of (SML)
return

13% .
Risk Premium
11%
Market Risk Premium
This linear relationship
between risk and required
(7%) return is known as the
Risk- Risk Free Rate Capital Asset Pricing Model
(CAPM).
free
rate of 1.0 1.5 Beta 28
return