Portfolio Risk and Return: Part 2 Flashcards
Capital Market Line characteristics
- 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
Capital market line equation
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
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?
Sp = wm * Sm = 0.75 * 0.30 = 22.5% Rp = wRf *Rf + wm*Rm = 0.25 * 0.10 + .75 * 0.16 = 14.50%
Total risk (variance) =
total risk = systematic variance + nonsystematic variance
Systematic risk characteristics
- 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
Nonsystematic risk characteristics
- 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)
Beta characteristics and formula
- 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
CAPM formula and key assumptions
expected return = risk free rt + [ Beta * (expected market return - risk free rt) ]
re = rf + B(MRP)
- investors are risk-averse, utility-maximizing, and rational
- markets are frictionless
- all investors plan for a single holding period
- investors have homogenous expectations
- investments are infinitely divisible
- investors are price takers
The Security Market Line characteristics
- 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
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?
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%
Limitations of CAPM:
- 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
Sharpe ratio characteristics and formula
- 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
M-Squared ratio characteristics and formula
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
Treynor Ratio characteristics and formula
- 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
Jensen’s Alpha characteristics and formula
- 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) ) ]
Beta formula
B = Corr between the stock and market * Stdv of the stock / Stdv of the market
= Corr * Si / Sm
Risk governance
Rick tolerance
Risk budgeting
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
Security Characteristic Line (SCL), characteristics
- 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) ]
Portfolio construction; diversifying a portfolio characteristics
- 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
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 ...
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
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?
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
