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1. SECTION II
Portfolio
Management

2. CHAPTER 14
Portfolio Risk and
Performance
Attribution

3. CHAPTER AGENDA
▪ Explain, interpret, and calculate basic statistics such as expected
value, variance, standard deviation, covariance, and correlation.
▪ Calculate and interpret the expected return and standard
deviation of a stock portfolio and compare investment portfolios
based on mean/variance efficiency.
▪ Identify the subcomponents of portfolio volatility, interpret the
type of risk each subcomponent represents, and explain why
only one of the subcomponents is affected by diversification.
▪ Identify and explain the two key drivers of beta.
▪ Interpret the concept of beta in a linear regression context.
3

4. CHAPTER AGENDA
▪ Explain why investing in stocks with solid fundamentals naturally
leads to a low-beta portfolio.
▪ Explain how a portfolio’s active sector weights can cause it to
under- or outperform its benchmark index.
▪ Explain how comparing a fund’s sector returns to the returns of
the corresponding SPDR sector exchange-traded funds (ETFs)
can illustrate how effective the fund’s managers are as active
investors.
▪ Calculate and interpret the Sharpe and Treynor ratios for
individual stocks and stock portfolios.
▪ Explain how multifactor models represent an alternative
approach to analyzing a portfolio’s returns and exposure to risk.
4

5. Foundations: Risk and Expected Return
▪ Markowitz‘s analysis employed several assumptions, the most important of
which are:
▪ Investors are generally risk-averse.
▪ They base their portfolio decisions on risk and expected return only.
▪ They measure risk as the variance (or standard deviation) of expected returns.
Expected Value and Expected Returns
▪ If we believe that the annual return histories of the four stocks represent an
appropriate basis, we can calculate the arithmetic mean return for each stock and
conceptualize these historical averages as each stock‘s forward-looking
expected return for the next period
5 Total Risk = Volatility = Standard Deviation of Returns

6. Standard Deviation
The Standard Normal Distribution.
6
▪ The normal distribution,
sometimes called the bell
curve, is symmetric around its
central value, the arithmetic
mean (as well as the median
and mode, as these are all
equal for normal
distributions).
▪ Time series with higher
standard deviations are
therefore more risky (have
higher volatility), and
▪ Time series with lower
standard deviations are less
risky, or less volatile
The Standard Normal Distribution.

7. Standard Deviation - Calculation
7
Expected Value and Expected Returns
Variance
Standard Deviations

8. The Components of Volatility
▪ The Market or macroeconomic driver of volatility is also called ―systematic‖ risk
▪ The firm-specific component of volatility is sometimes referred to as
―unsystematic‖ risk, denoting that this type of news pertains to the company
only.
▪ We have to understand how intelligent diversification makes an investment
portfolio more ―mean/variance efficient‖—generating higher returns per unit of
risk, or having lower volatility per unit of return
8

9. Statistical Representations of Macroeconomic and Firm-Specific Risk
▪ Standard deviation (or variance) of returns will therefore represent firm specific
risk in the portfolio risk calculations that follow
▪ Portfolio risk metric that reflects how companies‘ stock returns move together
and co-respond to macroeconomic news we need Covariance.
▪ The variance and covariance formulas are nearly identical, with one exception:
when calculating covariance, instead of multiplying the first stock‘s deviation
from its mean in each period by itself. we multiply it times the second stock‘s
deviation from its mean.
▪ if variance measures how one stock varies around its own mean, covariance
measures how two stocks co-vary around their respective means.
▪ Covariance will take a positive value if the returns of two stocks tend to move
together, or more precisely, if they tend to be above and below their means at
the same time.
▪ Conversely, if the returns of two stocks tend to move oppositely, meaning that
when one is above its mean the other tends to be below its mean (and vice
versa), covariance will take a negative value.
9

10. Statistical Representations of Macroeconomic and Firm-Specific Risk
▪ covariance is the key input to another statistic that is important in understanding
how diversification reduces risk, and is also much easier to interpret: the
correlation coefficient
▪ The lowest value the correlation coefficient can take is −1.0 (indicating perfect
negative correlation), and the highest value is +1.0 (indicating perfect positive
correlation).
▪ When the correlation coefficient is close to the midpoint of the range (zero), the
interpretation is that the two series have no reliable statistical relation, either
positive or negative.
▪ calculation of the correlation coefficient between the returns of CVX and JNJ,
which, as we expected, is low at 0.091. (Although the correlation coefficient is
technically an index ranging from −1.0 to +1.0, it will sometimes be referred to as
a percentage, which would be 0.091%
10

11. How Diversification Reduces Risk (Why Only Firm-Specific Risk Reduced)
▪ How the variance and covariance terms proliferate as the number of stocks in a
portfolio increases will be the key to understanding how diversification reduces
risk, and why only the firm-specific risk component of portfolio volatility is
reduced.
▪ Diversifying a Portfolio with CVX, YUM, and JNJ
11

12. How Diversification Reduces Risk (Why Only Firm-Specific Risk Reduced)
12

13. Sharpe Ratio
13
▪ The Sharpe ratio is calculated as an investment‘s excess investment return
(above the prevailing riskfree rate) divided by its standard deviation of returns

14. Three-Asset portfolio
14
▪ JNJ has a low correlation with CVX (+0.09, similar to YUM‘s −0.02), and an
extremely low correlation with YUM of −0.74.

15. BETA
15
▪ We‘ll gain by measuring and managing portfolio risk using beta instead of
Markowitz‘s mean variance framework:
▪ Beta can be interpreted as an index that measures how much volatility a stock
will contribute to a diversified portfolio. This will allow us to rank every stock’s
potential contribution to portfolio volatility using the same index scale.
▪ Beta is also a scaled version of covariance, and equally easy to interpret.
▪ The average beta of all stocks in the market will always equal 1.0, thus stocks
with betas above 1.0 will be “high-beta,” and stocks with betas below 1.0 will be
“low-beta.”
▪ We’ll only need to calculate n betas—one for each stock. In terms of risk
management, adding (deleting) a stock with a beta greater than the portfolio’s
weighted average beta will increase (decrease) portfolio volatility, and vice versa
if we add or delete stocks with betas less than the portfolio’s average beta.
▪ The portfolio’s weighted average beta will be our measure of the portfolio’s
exposure to macroeconomic risk.

16. Performance Attribution: Sector Weights,
Dividend Yield, Beta, and Style
▪ The students have
managed the fund as a
genuine buy-and-hold
portfolio since its
inception. Their goal is
to trade and reinvest
no more than 25 to
30% of the portfolio‘s
net asset value per
year, versus an average
turnover rate of 100%
for professionally
managed mutual funds.
16

17. Performance Attribution: Sector Weights,
Dividend Yield, Beta, and Style
17
Sector Under- and Overweights

18. Performance Attribution: Sector Weights,
Dividend Yield, Beta, and Style
18
Student Investment Fund Dividend Yield by Sector

19. Portfolio Alpha and Beta
▪ The stability of a fundamentals-based portfolio are evident from the graph. As
the market accumulated losses totaling almost −50% by March 2009, the SIF
experienced a decline of only −32%.
▪ Over the entire five-year period shown, the SIF earned a total return of 16.2%
while the S&P 500 index increased 16.6% (3.04% and 3.12% annualized,
respectively). The students therefore matched their benchmark based on total
returns over the fiveyear period.
19

20. Portfolio Alpha and Beta
▪ The regression model is depicted as Equation
▪ The regression fits the data well, resulting in an R-squared of 75.0%, which
indicates that the excess returns of the S&P 500 explain 75% of the variation in
the excess returns of the SIF.
▪ The regression fits the data well, resulting in an R-squared of 75.0%, which
indicates that the excess returns of the S&P 500 explain 75% of the variation in
the excess returns of the SIF.
▪ The regression intercept equals 0.11% — this is the portfolio‘s alpha, indicating a
small average monthly outperformance (1.001112 − 1 = 1.33% annualized).
▪ The regression beta coefficient equals 0.67, which indicates that the SIF earned
these returns with only two-thirds of the volatility of the S&P 500.
▪ The SIF‘s low beta is earned mainly during the market‘s bear phase, when the
fund‘s losses (−32%) are only about two-thirds of the market‘s losses (−50%).
This is exactly the type of conservative, low-volatility performance
20

21. Sector Betas and the Treynor Ratio
▪
21

22. Multifactor Models
▪ we used a single-factor performance attribution model that compared the
excess returns of a portfolio to the excess returns of an index benchmark. We
measured excess returns as the intercept of the regression model (alpha) and
risk as the slope of the line of best fit (beta)
▪ Multifactor Models Based on Macro Factors.
▪ Multifactor models take a variety of approaches in an attempt to understand the
forces that determine a portfolio‘s returns.
▪ A portfolio manager would use a multifactor macro model when he believes that
it‘s important to understand how the returns of a portfolio might respond to
individual macro factors. Macro multifactor models are used more often in a
quantitative portfolio management process.
22

23. Multifactor Models Based on Macro Factor
▪ 1. Rm − RFthe monthly excess return to the S : &P 500 index
▪ 2. ΔIPthe monthly percentage change in U.S. industrial production :
▪ 3. ΔCPIthe monthly percentage change in the U.S. consumer price index
▪ 4. ΔBaa − RFthe monthly percentage change in the bond credit spread (Baa yield −
risk-free rate) :
▪ 5. Δ30yr − RFthe monthly percentage change in the slope of the term structure of
interest rates (30-year T-bond yield − risk-free rate). :
23

24. Multifactor Models Based on Style Factors
▪ The model, expresses the excess returns of a stock or a
portfolio as a function of the following factors:
▪ 1. Rm − RFthe monthly excess return to the S : &P 500
index
▪ 2. SMB: “small minus big,” equal to the returns to a small-
capitalization portfolio minus the returns to a large-
capitalization portfolio
▪ 3. HML: “high minus low,” equal to the returns to a portfolio
of stocks with high book-to-market ratios minus the
returns to a portfolio of stocks with low book-to-market
ratios
▪ 4. MOM: momentum, equal to the returns to a portfolio of
stocks with the best performance over the past year
minus the returns to a portfolio of stocks with the worst
performance
24

25. Managing a Portfolio Using Multifactor Models
▪ Multifactor models provide different frameworks for managing investment
portfolios. Practitioners often refer to the various risk categories to which they
seek or avoid exposure as buckets
▪ Our preferred method for portfolio management (heavily emphasized in this
chapter) is the sector allocation approach.
▪ The wealth invested in our portfolio as being allocated among 10 possible sector
―buckets.
▪ Similarly, managers implementing a more quantitatively focused process think in
terms of adding stocks with strong exposure to desirable macro factors, and
trimming positions that provide exposure to less desirable macro factors.
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26. Points to be Remember
 CAPM – Asset Pricing Model
 The Capital Asset Pricing Model (CAPM) is a model
that describes the relationship between the
expected return and risk of investing in a security.
 It shows that the expected return on a security is
equal to the risk-free return plus a risk premium,
which is based on the beta of that security.
Ra = Expected return on a security
Rrf = Risk-free rate
Ba = Beta of the security
Rm = Expected return of the market
Note: “Risk Premium” = (Rm – Rrf)

27. Points to be Remember
Standard Deviation
 Portfolio Standard Deviation is the standard
deviation of the rate of return on an investment
portfolio and is used to measure the inherent
volatility of an investment. It measures the
investment’s risk and helps in analyzing the stability
of returns of a portfolio.
 Portfolio Standard Deviation refers to the volatility of
the portfolio which is calculated based on three
important factors that include the
 standard deviation of each of the assets present in
the total Portfolio,
 the respective weight of that individual asset in
total portfolio and
 correlation between each pair of assets of the
portfolio.

28. Points to be Remember
Portfolio Alpha
 The alpha of a portfolio is the excess return it
produces compared to a benchmark index.
Alpha of portfolio = Actual rate of return of portfolio –
Risk-free rate of return – β * (Market return – Risk-free
rate of return)
 A positive alpha of 5 (+5) means that the portfolio’s
return exceeded the benchmark index’s
performance by 5%.
 An alpha of negative 5 (-5) indicates that the
portfolio underperformed the benchmark index by
5%.
 The alpha ratio is often used along with the beta
coefficient, which is a measure of the volatility of an
investment.

29. Points to be Remember
Portfolio Beta
 Portfolio beta is a measure of the overall systematic
risk of a portfolio of investments. It equals the
weighted-average of the beta coefficient of all the
individual stocks in a portfolio.
 The Beta coefficient is a measure of sensitivity or
correlation of a security or an investment portfolio to
movements in the overall market.
 A beta coefficient can measure the volatility of an
individual stock compared to the systematic risk of
the entire market.
 If the Beta of an individual stock or portfolio equals
1, then the return of the asset equals the average
market return.

30. Points to be Remember
Variance & Co Variance
 Variance refers to the spread of a data set. It’s a
measurement used to identify how far each number in the
data set is from the mean.
 A large variance means that the numbers in a set are far
from the mean and each other.
 A small variance means that the numbers are closer
together in value.
 Covariance is a measure of the relationship between
two random variables. The metric evaluates how much – to
what extent – the variables change together.
 Covariance, we can only gauge the direction of the
relationship (whether the variables tend to move in tandem
or show an inverse relationship).
 Positive covariance: Indicates that two variable tend to
move in the same direction.
 Negative covariance: Reveals that two variables tend to
move in inverse directions.

31. Points to be Remember
Correlation coefficients
Correlation coefficients are indicators of the strength of the
linear relationship between two different variables, x and y.
 The possible range of values for the correlation coefficient
is -1.0 to 1.0.
 A linear correlation coefficient that is greater than zero
indicates a positive relationship.
 A value that is less than zero signifies a negative
relationship.
 Finally, a value of zero indicates no relationship between
the two variables x and y.

32. Points to be Remember
Sharpe Ratio
Sharpe Ratio is commonly used to gauge the performance of
an investment by adjusting for its risk.
The higher the ratio, the greater the investment return relative
to the amount of risk taken, and thus, the better the investment.
The ratio can be used to evaluate a single stock or investment,
or an entire portfolio.
Sharpe Ratio Grading Thresholds:
Less than 1: Bad
1 – 1.99: Adequate/good
2 – 2.99: Very good
Greater than 3: Excellent

33. Points to be Remember
Treynor Ratio
Treynor Ratio is a portfolio performance measure that adjusts
for systematic risk.
In contrast to the Sharpe Ratio, which adjusts return with the
standard deviation of the portfolio , the Treynor Ratio uses the
Portfolio Beta, which is a measure of systematic risk.
A higher ratio indicates a more favorable risk/return scenario.
Keep in mind that Treynor Ratio values are based on past
performance that may not be repeated in future performance.
Treynor Ratio measures portfolio performance and is part of the
Capital Asset Pricing Model.

34. Thanks