Made for the easiness of others. :)

1. RISK MANAGEMENT
Risk and Return
Presented by:
AsHra ReHmat

2. Risk
• Risk is defined as the chance that an
investment's actual return will be different
than expected.
This includes the possibility of
losing some or all of the original investment.
OR
• The variability of returns from those that are
expected.

3. Return
• Income received on an investment plus any
change in market price, usually expressed as a
percent of the beginning market price of the
investment.
Dt + (Pt - Pt-1 )
Pt-1
R =

4. Expected return
• Expected return is calculated as the weighted
average of the likely profits of the assets in the
portfolio, weighted by the likely profits of each
asset class.
E(R) = w1R1 + w2R2 + ...+ wnRn

5. Example
Assume an investment manager has created a
portfolio with Stock A and Stock B. Stock A has an
expected return of 20% and a weight of 30% in
the portfolio. Stock B has an expected return of
15% and a weight of 70%. What is the expected
return of the portfolio?
E(R) = (0.30)(0.20) + (0.70)(0.15)
= 6% + 10.5% = 16.5%
The expected return of the portfolio is 16.5%.

6. Portfolio
• A portfolio is a grouping of financial assets such as
stocks, bonds and cash equivalents.
• Portfolios are held directly by investors or managed by
financial professionals.
• Investors should construct an investment portfolio in
accordance with their risk tolerance and investing
objectives.
• Think of an investment portfolio as a pie that is divided
into pieces of varying sizes representing different asset
classes and/or types of investments to accomplish an
appropriate risk-return portfolio allocation.

7. Variance
Variance (σ2) is a measure of the dispersion of a
set of data points around their mean value.
It is computed by finding the probability-
weighted average of squared deviations from the
expected value.
Variance measures the variability from an
average (volatility). Volatility is a measure of risk,
so this statistic can help determine the risk an
investor might take on when purchasing a specific
security.

8. Example: Variance
Assume that an analyst writes a report on a company and,
based on the research, assigns the following probabilities to
next year's sales:
The analyst's expected value for next year's sales is (0.1)*(16.0)
+ (0.3)*(15.0) + (0.3)*(14.0) + (0.3)*(13.0) = $14.2 million.
Scenario Probability
(P)
Sales ($ Millions)
E(R)
1 0.10 $16
2 0.30 $15
3 0.30 $14
4 0.30 $13

9. Calculating variance starts by computing the difference
in each potential sales outcome from $14.2 million,
then squaring:
Scenario Probability
(P)
Deviation from Expected
Value
( R-R )
Squared
1 0.10 (16.0 - 14.2) = 1.8 3.24
2 0.30 (15.0 - 14.2) = 0.8 0.64
3 0.30 (14.0 - 14.2) = - 0.2 0.04
4 0.30 (13.0 - 14.2) = - 1.2 1.44
Variance then weights each squared deviation by its probability, giving us the
following calculation:
(0.1)*(3.24) + (0.3)*(0.64) + (0.3)*(0.04) + (0.3)*(1.44) = 0.96

10. Correlation Coefficient
A standardized statistical measure of the
linear relationship between two variables.
Its range is from -1.0 (perfect negative
correlation), through 0 (no correlation), to
+1.0 (perfect positive correlation).

11. 'Diversification'
• A risk management technique that mixes a
wide variety of investments within a portfolio.
“Don’t put all your eggs in one basket”

12. Diversification and the Correlation
Coefficient
INVESTMENTRETURN
TIME TIMETIME
SECURITY E SECURITY F
Combination
E and F
Combining securities that are negatively
correlated reduces risk.

13. Total Risk = Systematic Risk +
Unsystematic Risk
Systematic Risk is the variability of return on
stocks or portfolios associated with changes in
return on the market as a whole.
Unsystematic Risk is a risk unique to a particular
company or industry; it is independent of
economic, political and other factors that affect
all securities in a systematic manner.
It is avoidable through diversification.
Total Risk = Systematic Risk + Unsystematic Risk

14. Total Risk = Systematic Risk +
Unsystematic Risk
Total
Risk
Unsystematic risk
Systematic risk
STDDEVOFPORTFOLIORETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors such as changes in nation’s
economy, tax reform by the Congress,
or a change in the world situation.

15. Total Risk = Systematic Risk +
Unsystematic Risk
Total
Risk
Unsystematic risk
Systematic risk
NUMBER OF SECURITIES IN THE PORTFOLIO
STDDEVOFPORTFOLIORETURN
Factors unique to a particular company
or industry. For example, the death of a
key executive or loss of a governmental
defense contract.

16. Capital Asset
Pricing Model (CAPM)
• This model was developed in 1960s by
Nobel Laureate William Sharpe.
• CAPM is a model that describes the
relationship between risk and expected
(required) return; in this model, a
security’s expected (required) return is
the risk-free rate plus a premium based
on the systematic risk of the security.

17. Characteristic Line
EXCESS RETURN
ON STOCK
EXCESS RETURN
ON MARKET PORTFOLIO
Beta
Narrower spread
is higher correlation
Characteristic Line

18. What is Beta?
An index of systematic risk.
It measures the sensitivity of a stock’s returns to
changes in returns on the market portfolio.
The beta for a portfolio is simply a weighted
average of the individual stock betas in the
portfolio.

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

20. Security Market Line
Rj = Rf + bj(RM - Rf)
Rj is the required rate of return for stock j,
Rf is the risk-free rate of return,
bj is the beta of stock j (measures systematic risk
of stock j),
RM is the expected return for the market
portfolio.

21. Security Market Line
Rj = Rf + bj(RM - Rf)
bM = 1.0
Systematic Risk (Beta)
Rf
RM
RequiredReturn
Risk
Premium
Risk-free
Return

22. Determination of the Required Rate
of Return
Lisa Miller at Basket Wonders is attempting to
determine the rate of return required by their
stock investors. Lisa is using a 6% Rf and a
long-term market expected rate of return of
10%. A stock analyst following the firm has
calculated that the firm beta is 1.2. What is
the required rate of return on the stock of
Basket Wonders?

23. BWs Required Rate of Return
RBW = Rf + bj(RM - Rf)
RBW = 6% + 1.2(10% - 6%)
RBW = 10.8%
The required rate of return exceeds the market
rate of return as BW’s beta exceeds the market
beta (1.0).