CAPM 1 Flashcards
(19 cards)
CAPM assumptions
-Investors are rational, mean variance optimisers
-Single period planning horizon
-investors have homogeneous expectations. the same beliefs about future returns, risks, and correlations of assets
-All assets are publicly traded; short selling is allowed.
-Investors can borrow/lend at a common risk-free rate.
-No taxes or transaction costs.
Define beta, interpret values of beta and formula
-Beta is a measure of systematic risk of an asset, the responsiveness of changes in an assets returns to changes in the market returns.
-Formula:
-Bi = Pim * σi / σm
σi/m = SD of asset/market returns returns. Pim corr coeffient asset and market.
Also B = Cov(Ri, Rm) / Var(Rm)
-Interpretation:
-B > 1, stocks known as agressive/volatile compared to market.
-B = 1, asset returns moves in line with the market./ same volility as market.
-B= 0, Asset returns are uncorrelated with the market, no systematic risk.
-Beta isolates systematic risk, the part of total risk that cannot be diversified away and is due to market factors.
Portfolio beta
-Each asset within a portfolio has a beta, can be combined to form portfolio beta.
-measures portfolios overall systematic risk.
-Bp = Sum (wi * Bi), weight of stock and stock beta
Describe applications of the capm
- Measure portfolio performance using tools like Jensen’s Alpha.
-Estimate the cost of capital for firm investment projects, using required rate of return.
-Portfolio selction based on expected return vs. systematic risk
-Identify mispricing (over/undeervaluded shares) by comparing expected and required returns
Describe the sharpe ratio and why more widely used
-Refers to the excess (in the numerator) return per unit of risk, sd.
-Measure of risk adjusted return on investment.
(Rp - Rf )/ σp
-Sharpe Ratio is more widely used than Treynor because it accounts for total risk, penalizing poor diversification, while Treynor only considers market risk/systematic risk.
Describe the treynor ratio
-Measures excess return relative to systematic risk only (beta).
Refers to excess return per unit of systematic risk, beta.
= (Rp - Rf) / Bp
Describe the sortino ratio
-measures additional/excess return in excess of a selected minimum acceptable return threshold, per unit of downside negative risk.
-Focuses on only negative fluctuations rather than total risk (excludes gains.)
-ST = (Ri - t )/ DRi or ST = Ri - t / σd
where t is comparison rate, could be RFR and σd is standard deviation of downside risk.
Describe the information ratio
-Info Ratio shows how an investment performs compared to benchmark relative to the additional risk taken. Can be veiwed as a benefit to cost ratio.
-measures a portfolio’s average return in excess of a benchmark divided by the standard
deviation of this excess return.
-IR = (Rj - Rb)/ σER ,
σER = sd of excess return Rb average return on benchmark.
-numerator is ability to generate portfolio return, numerator shows risk taken to generate this excess return.
Good +ve, 1 exceptional
Describe jensens alpha
-measures how much a portfolio under or overperformas relative to predictions of the CAPM.
-Focuses on systematic risk/beta therefore doesnt account a managers ability to diversify.
Rit - Rf = ai + Bi(Rmt - Rf) + Eit
-rearrange for a (Rit = portfolio i return at time t, RM market return etc.)
α = 0 → Portfolio performs exactly as predicted by CAPM → in equilibrium
α > 0 → Portfolio outperforms CAPM predictions → suggests superior manager skill
α < 0 → Portfolio underperforms CAPM predictions → suggests poor manager performance
Describe estimated return and the SML for identyfing under/overvalued assets
-If an assets estimated return plots above the
SML, asset is underpriced/undervalued. Estimated > expected (capm) –> udnervalued
-If an assetsestimated return that plots below the
SML asset is overpriced/overvalued. Estimated < Expected (Capm) –> overvalued.
-In equilibrium, all assets/portfolios plot on the (SML). Properly valued estimated = expected
-Investors who find assets with estimated returns consistently above the SML can achieve superior risk-adjusted returns.
Formula for estimated return
-The estimated return is the return you expect based on information other than CAPM,
-R(estimated) = (P1 - P0) / P0 + D1/ P0
OR R = (Pt+1 - Pt) / Pt + Dt+1 / Pt
Define CAPM + formula + equilbirum
CAPM explains the relationship between an asset’s systematic risk and its expected return
-Ri = Rf + Bi(Rm-Rf)
-Ri = Required/expected return on asset i, Rm: Expected market return.
-In CAPM, required return = expected return when the market is in equilibrium
Challenges and limitations to portfolio theory which led to development of CAPM
-Port theory simple when N = 2, two assets.
Markowriz portfoltio thoery Requires calculating (N²–N)/2 covariance terms
High amount of accurate calcluations and estimates of required. needed with markowitz.
Limitations Led to simplification: Sharpe (1963) noted stocks move in varying degress with the market led to developement of CAPM by Lintner (1965)
Beta special cases 1 and no portfolio risk
-No variance in the portfolio 𝜎p = 0, then B = 0 and Rp = Rf.
-Beta = 1, 𝜎p = 𝜎M and Rp = Rm.
Why are risk adjusted metrics important for assessing investment performance?
-Fund may show high returns but past performace doesn’t equal future performance, assessing performance relative to risk taken on board is key.
-High returns may come with high volatility (eg +50%, -20%)
-Risk-adjusted metrics evaluate return relative to the risk taken, giving a fairer comparison between investments. Eg) sortino, information ratio, sharpe ratio, jensens alpha, treynor.
Describe downside risk (sortino ratio/sd of downside risk)
-Measures the volatility of returns below a threshold (mean, negatice etc), unlike normal standard deviation, which considers both gains and losses.
-Captures what investors consider truly risky.
-Semi-deviation is a common downside risk measure — it is the standard deviation of returns that fall below a specific threshold (typiclly the mean/expected return.)
-σd = sqrt[1/n * ∑ (Ri - R^)^2 ]
-Include RI if they fall below the threshold R. N number of returns below the threshold (typically mean)
Describe and compare the Capital market line CML and the security market line SML
-CML applies to only to efficient portfolios (combinations of the market portfolio and the risk-free asset whereas SML Applies to all individual securities and portfolios, efficient or not.
-CML uses total risk (Sd), SML uses systematic risk (beta).
-In equilibrium, all efficient portfolios lie on the CML, in equiblirum all securities/portfolios are priced to lie on the SML.
-CML is Relevant for portfolio construction and comparing portfolio performance. where as SML is Useful for asset pricing and identifying overvalued or undervalued securities.
Describe the security market line
-SML is a graphical representation of the Capital Asset pricing model CAPM. Return Beta sapce (R, B)
-Can dsplay the market portfolio when B =1
-Shows the relationship between expected return and its systematic risk (beta), pure time value of money Rf and the reward for bearing systematic risk, risk premium.
-SML displays the return to the ith security by relating its expected return to its beta.
Securities plotting on the SML are fairly priced.
Above the SML = undervalued; below = overvalued
Describe the process of deriving the CAPM
