Chapter 21 Flashcards
The math for calculating risk and return of port.
Calculation of Weight B asset & Formula.
In the previous reading, we covered the mathematics of calculating the risk and return of a portfolio with a PERCENTAGE weight of WA invested in a risky portfolio (P) and a weight of WB = 1 − WA invested in a risk-free asset.
Risk Free has zero standard deviation and zero correlation returns with risky port, it allows asset be to be risk-free and asset a to be risky which results in reduced equation. What is the equation?
Port expected return and Port Std. Dev when combo Rf with Risky asset
CML formula
Y-intercept formula
CML rewritten and interpretation.
Rf is the intercept
Slope is [E(Rm)-Rf / Sigma m]
Total Risk
total risk = systematic risk + unsystematic risk
Multifactor Model, interpretation, and which model uses it.
Factors (Fs) are the expected values of each risk factor
Betas are the assets factor sensitivities or factor loading for each risk factor.
Single factor/Index model
Simplified form of single-index model is market model. What is the formula:
3 parts
Fam and French 3-factor model risk factors
What is Beta
The sensitivity of an asset’s return to the return on the market index in the context of the market model is referred to as its beta.
Beta is a standardized measure of the covariance of the asset’s return with the market return
Beta Formula & What is it also known as.
This is also the slope of security characteristic line.
Beta Formula: Correlation between returns on asset i with returns on market index
Beta for market formula
Beta for market =
is corr of mrk by itself which is one * the risk of market with its self so tis 1.. .so this is relative sys risk of the market.
Market rept one unit of sys risk.. it has beta of 1, if stock have beta 2 , ti has twice the sys risk as market so that has implication of risk premium you should demand.
correlation between the returns on asset i with return on market index formula.
Get COVim formula
Substituting for COVim in equation for Beta i, we can calculate beta again as:
Example: Calculating an asset’s beta
The standard deviation of the return on the market index is estimated as 20%.
If Asset A’s standard deviation is 30% and its correlation of returns with the market index is 0.8, what is Asset A’s beta?
Example: Calculating an asset’s beta
The standard deviation of the return on the market index is estimated as 20%.
If the covariance of Asset A’s returns with the returns on the market index is 0.048, what is the beta of Asset A?
CAPM vs SML
CAPM what fair expected return it should be for a security given sys risk.
SML is the linear representation of CAPM.
Assumptions of CAPM
Side Notes:
- No compounding , just one period
- Equilibrium meaning everything is fairly price and everyone needs to be able to trade (divisible).
- All investor is price taker, meaning there is no one investor that is big enough to make the price.
SML/CAPM Equation
E(Rmrk) is the market return
So market premium is E(Rmrk)-Rf
Impact of systematic risk measured by BETA.
beta rewrriten with correlation formula
From CAPM formula, what is the stock risk premium
CML vs SML vs CAPM
CML is the TOTAL risk and its a tool to measure efficiency of port.
- Investor use combo fo risk free + mrk port.
- CML slope is the sharpe ratio of market port.
- CML Bbased on TOTAL RISK
-CML has only efficient ports.
SML is the SYSTEMATIC risk.
- Appraiser tool to see if security is fairly valued.
- Security above SML means its UNDERVALUE
because its retuning too much compared to beta.
- Security is below SML it means its OVERVALUE bc
its not returning enough relative to its beta.
- ANY ASSET or PORT. plots on the sml in equalbirium
- SML based on SYSTEMATIC RISK which is BETA
CAPM is expected return on asset based ONLY on beta (sys risk). CAPM gives us a number tells us what fiar return should be for security:
For stocks that are not fairly priced example:
Step (1) Get HPR
Step (2) Use CAPM Formula
High Sharpe Ratio means what?
The portfolio with the highest sharpe ratio is superior.
Sharpe Ratio Formula
CML Equation
CAL Slope and CML Slope Equations for Sharpe Ratios as Slopes
What is M-Squared
M-Squared is the portfolio return, if the portfolio had the same risk as the market…that return will be the formula.
For a portfolio of risky assets, M-squared (M2) is an alternative to the Sharpe ratio as a risk-adjusted rate of return, expressed as a percentage rather than as a slope.
M-Squared Formula
Interpretation for when:
M-Squared = to Mrk Return
M-Squared > Mrk Return
The M^2 – is the port return, if port had same risk as market, that return will be the formula.
If M^2 is = to market return, then you have a port that is fairly priced.
If M^2 > Mrk return, we have superior port. , Port P has sharpe ratio greater than the slope or sharpe ratio of the market.
M-Squared Alpha Definition.
The extra return on the Portfolio P* above the return on the market portfolio, (P* – RM), is referred to as M2 alpha.
How is M-Squared Port created?
M-Squared for a Portfolio, P* is created by BORROWING at Rf and investing the proceeds in Portfolio P, in an amount so that the standard deviation of P* = σM.
Jenson Alpha
No Random
The difference between forecasted return and required return from CAPM formula
Treynor Measure
Treynor Measure – higher means you are getting paid more per unit of SYSTEMATIC RISK
The slope/sharpe ratio is the treynor measure.
Two measures of portfolio performance based on systematic (beta) risk rather than total risk are the Treynor measure and Jensen’s alpha.
Treynor vs Jensons
Treynor measure is a measure of slope and Jensen’s alpha is a measure of percentage returns in excess of those from a portfolio that has the same risk (beta) but lies on the SML.
Treynor Formula and interpretation
Jensens Alpha Formula and interpretation
Jenson Alpha: How much you are outperforming the fair return which is the SML
Expected Port Return (Rp) – Fair Return WHICH IS [Rf + Beta P (Rmrk – Rf) ]
Example Question:
The risk-free rate is 6%, and the expected market return is 15%. A stock with a beta of 1.2 is selling for $25 and will pay a $1 dividend at the end of the year. If the stock is priced at $30 at year-end, it is:
required rate = 6 + 1.2(15 − 6) = 16.8%
return on stock = (30 − 25 + 1) / 25 = 24%
Based on risk, the stock plots above the SML and is underpriced, so buy it.
A stock with a beta of 0.7 currently priced at $50 is expected to increase in price to $55 by year-end and pay a $1 dividend. The expected market return is 15%, and the risk-free rate is 8%. The stock is:
required rate = 8 + 0.7(15 − 8) = 12.9%
return on stock = (55 − 50 + 1) / 50 = 12%
The stock falls below the SML so it is overpriced
Which of the following is the vertical axis intercept for the Capital Market Line (CML)?
The CML originates on the vertical axis from the point of the risk-free rate.
(Module 21.1, LOS 21.b)
The expected rate of return is 1.5 times the 16% expected rate of return from the market. What is the beta if the risk free rate is 8%?
1.5*.16 = .24
Formula is SML formula
E(Ri) = Rf + Bi [ E(Rmrk) - Rf]
24 = 8 + B (16-8)
24= 8 + B (8)
24-8 = 8 B
16 = 8 B
B= 16/8 = 2
An analyst has estimated the following:
Correlation of Bahr Industries returns with market returns = 0.8
Variance of the market returns = 0.0441
Variance of Bahr returns = 0.0225
The beta of Bahr Industries stock is closest to:
Which of the following measures produces the same portfolio rankings as the Sharpe ratio but is stated in percentage terms?
M-squared measures the excess return of a leveraged portfolio relative to the market portfolio and produces the same portfolio rankings as Sharpe ratio.
SML Equation rearranged to get the expected return on market
RR is required return
R is return
Rf is risk-free rate
SML Equation:
RR Stock = Rf + Beta [ E(Rmrk) - Rf ]
Rearranged :
E(Rmrk) = [RR Stock - Rf + (BetaStock * Rf) ]
———————————————
Beta Stock
Total risk is measured by what and systematic risk is measured by what?
TOTAL RISK is measured by SD
Sys risk is measured by beta.
The Market Model
Return gen model are used to estimated expected return on risky securities based on specific factors.
A simplified single- index model is what we call market model, used to estimate security or port beta, and estimate securities abnormal return which is the Ei, which si the return above its expected return based on actual market return.
Ri is return on our asset
Alpha is the y intercept
Beta is sensitivities of an asset return to the market. So slop increase if beta goes up because we want to be compensated for our risk. Higher risk = higher slope = higher expected rate of return.
Rmkt is Return on Market
Ei is the abnormal return or company specific return
One risk factor we look at is mrk return.
Estimating beta with market model.
What dose higher beta mean?
Higher beta, greater the risk, and higher the slope.
Market has beta of 1… so if beta > 1 that exhibit greater mrk risk and <1 is exhibit less than market risk.
Security Characteristic Line
is a plot of excess returns of a security, on the excess return on the market.
What is port beta?
Its the value-weighted average of port assets beta
Stock Risk Premium from CAPM Formula
Port Performance Evaluation
Four
What do they use to measure risk?
Sharpe
-Use SD
Treynor
-Use beta as risk measure
Msquared is alternative to sharpe
-Expressed as % vs slope
-Use SD
Jensen
-Also %
-Use beta as risk measure
