Portfolio Risk and Return: Part 2

Question 1

Capital Market Line characteristics

Answer 1

• its a special case of the CAL where the efficient portfolio is the “market portfolio”
• the market portfolio is the point where the CML is tangential to the efficient frontier
• CML intersects the y-axis at the RF rate

y-axis: portfolio expected return
x-axis: portfolio stdv

equation: Y = C + mX

Question 2

Capital market line equation

Answer 2

Y = C + mX

Y = portfolio return
C = Rf rt
m = slope = (Rm - Rf) / market stdv ----- this is aka the sharpe ratio
X = portfolio stdv

=
Rp = Rf + ((Rm - Rf) / Smarket) * Sp

Question 3

Client wants to build a portfolio with T-bills and an index fund. The T-bills have a return of 10%, the index fund expects to return 16% with a stdv of 30%. 75% of the portfolio will be in the index. What is the risk and return of this portfolio?

Answer 3

Sp = wm * Sm = 0.75 * 0.30 = 22.5%
Rp = wRf *Rf + wm*Rm = 0.25 * 0.10 + .75 * 0.16 = 14.50%

Question 4

Total risk (variance) =

Answer 4

total risk = systematic variance + nonsystematic variance

Question 5

Systematic risk characteristics

Answer 5

• non-diversifiable
• aka market risk that affects the entire economy
• aka beta risk
• investors get paid for systematic risk
• ex: interest rates, inflation, natural disasters, unrest/coup attempts

Question 6

Nonsystematic risk characteristics

Answer 6

• risk that can be diversified away
• ex: oil discoveries, non-approval for a drug, new regulations
• can be avoided
• does not earn a return
• there is no nonsystematic risk in a market portfolio (market index)

Question 7

Beta characteristics and formula

Answer 7

• a measure of systematic risk (market risk)
• tells us how sensitive an asset’s return is to the market as a whole
• estimated using linear regression
  
  • y-axis: security return (Ri)
  • x-axis: market return (Rm)
  • slope of the line is Beta
  • intersects at alpha (excess returns of the stock)

B = Cov(i,m) / variance of market return

B = corr of the security and market * stdv of the security / stdv of the market

Question 8

CAPM formula and key assumptions

Answer 8

expected return = risk free rt + [ Beta * (expected market return - risk free rt) ]
re = rf + B(MRP)

1. investors are risk-averse, utility-maximizing, and rational
2. markets are frictionless
3. all investors plan for a single holding period
4. investors have homogenous expectations
5. investments are infinitely divisible
6. investors are price takers

Question 9

The Security Market Line characteristics

Answer 9

• is a graphical representation of the CAPM model and applies to all securities, whether they are efficient or not
  - CML applies only to efficient portfolios
  - SML applies to any security and/or inefficient portfolios
  y-axis: expected retrurn; SML intersects at the rf rate
  x-axis: Beta (market risk)

the slope of SML is the market risk premium

Question 10

Client wants to invest 10% in the rf asset, 40% into a mutual fund which tracks the market, and 50% into a high-risk stock with a beta of 2.5. The rf = 5%, and the expected market return is 10%.
What is the portfolio beta and expected retrun?

Answer 10

rf asset: w=.1, return = .05, B=0
mutual fund: w=.4, r=10%, B=1
high-risk asset: w=.5, r=?, B=2.5

portfolio beta = .1 * 0 + .4 * 1 + .5 * 2.5 = 1.65; weighted avg beta of all assets

portfolio return = rf + B*(MRP) **use portfolio beta
= .05 + 1.65 * (.1 - .05) = 13.25%

Question 11

Limitations of CAPM:

Answer 11

• single-factor model
• single-period model
• different analysts use different proxies for the same asset
• CAPM is forward-looking, but Beta is historical
• assumes investors have the same expectations for securities

Question 12

Sharpe ratio characteristics and formula

Answer 12

• ratio of excess return of the portfolio - the risk free rate / portfolio risk
• measures the excess return per unit of risk
• higher ratio is better, but must be compared
• it is the slope of the capital allocation line (CAL)
• represents the reward-to-variability ratio
• the most widely recognized and used appraisal measure

*a total risk measure; can be used when a portfolio is not fully diversified

limitations

• uses total risk, not systematic risk
• it must be compared with another to see which is better

Sharpe = portfolio risk premium / portfolio total risk

         = Rp - Rf / Sp

Question 13

M-Squared ratio characteristics and formula

Answer 13

aka the risk-adjusted performance measure (RAP)

• is an adjustment to the Sharpe ratio
• greater than zero means the portfolio has positive risk-adjusted return
• if 0, the portfolio has the same risk-adjusted return as the market
• the result is in units of the percent return, which is more intuitive for interpretation

*a total risk measure; can be used when a portfolio is not fully diversified

limitation
- uses total risk and not systematic risk

M-Squared = [ (Rp - Rf) * Sm/Sp ] + Rf

               = (Sharpe ratio * Sm) + Rf

Question 14

Treynor Ratio characteristics and formula

Answer 14

• ratio of excess return of the portfolio - risk free rate / the systematic risk of the portfolio
• the numerator must be positive for meaningful results
• wont work with negative beta assets
• the equation is the same as the Sharpe ratio, but divides by systematic risk of the portfolio (B)

*based on beta risk and should be used when a portfolio is well diversified

limitations

• not informative; when two portfolios are compared, we know which is superior, but dont know if its performance is better than the market portfolio
• does not provide information about the amount of underperformance or over performance

Treynor ratio = ( Portfolio risk premium / portfolio beta risk )

                   = Rp - Rf / Bp

Question 15

Jensen’s Alpha characteristics and formula

Answer 15

• is the difference between the actual return on a portfolio and the CAPM (expected or required return)
• the plot of the excess return of a security on the excess return of the market
• based on systematic risk (like the Treynor ratio)
• the output (alpha) is used to rank managers and their porfolios
• since it uses systematic risk, it is theoretically superior to M-Squared

*based on beta risk and should be used when a portfolio is well diversified

JA > 0; the manager (portfolio) has positive risk-adjusted retrun than the market
JA = 0; the manager (portfolio) has the same risk-adjusted retrun as the market
JA < 0; the manager (portfolio) has lower risk-adjusted retrun than the market

Jensen’s Alpha = ( actual portfolio return - expected return )
= actual portfolio return - CAPM

                        = Rp - [ Rf + ( B * (Rm - Rf) ) ]

Question 16

Beta formula

Answer 16

B = Corr between the stock and market * Stdv of the stock / Stdv of the market
= Corr * Si / Sm

Question 17

Risk governance
Rick tolerance
Risk budgeting

Answer 17

risk governance
- aligning risk management with the goals of the entire organization
- a top-down approach; frim risk tolerance is determined, followed by providing risk oversight and guidance
to align risk with enterprise goals

risk tolerance
- is best discussed before awareness of risk is heightened

risk budgeting
- helps determine how or where risks are taken and quantifies tolerable risks by specific metrics

Question 18

Security Characteristic Line (SCL), characteristics

Answer 18

• can be used for security selection
• the security is undervalued it it plots above the SML (buy)
• the security is overvalued if it plots below the SML (sell)

y-axis: “excess security return”; Ri - Rf
x-axis: “excess market return”; Rm - Rf
slope: is the security’s Beta and intersects at alpha (alpha: Jensen’s alpha or excess return)

SCL: Ri - Rf = ai + [ Bi * (Rm - Rf) ]

Question 19

Portfolio construction; diversifying a portfolio characteristics

Answer 19

• holding as few as 30 stocks can diversify away the non-systematic risk

y-axis: variance
x-axis: number of stocks
line starts high at the top left and curves down as the number of stocks increases to 30
- the total variance is high with a low number of stocks
- non-systematic variance decreases as the number of stocks increases
- the line flattens at the rate of systematic variance

Question 20

An analyst has the following data:
Rf rate                                    5%
expected Rm                         12%
B of stock ABC                      1.3
current price of ABC             $20
yr end forecast of ABC         $22
dividend payment                 $2 
Based on price and dividend forecast, the analyst should ...

Answer 20

first, find the required return for ABC with CAPM
CAPM (Re) = Rf + B*(MRP)
= .05 + ( 1.3 * (.12 - .05))
Re = 14.1%

next, find the forecasted return of ABC
$EOY - $now + $Div / $now
= 22 - 20 + 2 / 20
= 20% return

since the forecasted return is > required return, the analyst should buy
- ABC will plot above the SML and is hence undervalued

Question 21

Stock A B C
Expected return 10.68% 16.30% 12.16%
Beta 1.3 1.6 .8
The Rf is 3.5% and the expected market return is 11.5%
Which stock is overvalued?

Answer 21

Find the required return for each stock using CAPM
- use the expected market return of 11.5% in the model and compare that to the individual expected return
re = rf + (B * MRP)
A: re = 3.5 + 1.3 * (11.5 - 3.5) = 13.9% required return
B: re = 3.5 + 1.6 * (11.5 - 3.5) = 16.3% required return
C: re = 3.5 + 0.8 * (11.5 - 3.5) = 9.9% required return

A: re 13.9 > 10.68 expected = overvalued
B: re 16.3 = 16.3 expected = at value
C: re 9.9 < 12.16 expected = undervalued