Misc Flashcards
(24 cards)
CAPM formula
ERi = Rf + bi(ERm - Rf)
r= rf+b(rm - rf)
-expected return of asset/portfolio = RFR + beta asset * market risk premium (expected return market - RFR)
define sharp ratio + in terms of market portfolio
-how much excess return an investor is receiving for each unit of risk taken sd.
-tells you how much excess return the market portfolio is generating compared to the risk-free rate for each unit of market risk (standard deviation of the market returns).
-slope of the cml
The optimal portfolio is identified at the point of tangency between the efficient frontier and the
-highest possible utility curve
Markowitz portfolio equilbirum outcome
in equilibrium, regardless of individual preferences, all investors will hold a combination of the market portfolio (M) and the risk-free asset (RFR). Investors may adjust positions by borrowing or lending at RFR in order to maximize their utility, depending on their individual risk level.
- Sharpe ratio
-Refers to the excess return per unit of risk, sd.
-Measure of risk adjusted return on investment.
Rp - Rf / σp
Treynor ratio/measure + why more widely used
-Measure of risk adjusted return on investment.
-Refers to additional/excess return per unit of systematic risk, beta. More widely used as penalises low diversification.
= Rp - Rf / Bp
- Information ratio/measure
-Ratio shows how an investment performs compared to benchmark relative to the additional risk taken.
IR = Rj - Rb / σER ,
σER = sd of excess return, numerator is ability to generate portfolio return > market, numerator shows risk taken to generate this excess return.
Good +ve, 1 exceptional
Securities with returns that lie above the security market line are
true
-If securities have returns (estimated) that sit above the SML they are –> undervalued.
-If securities with returns that lie below the SML are overvalued.
sortino ratio
-measure of risk adjusted performance and measures additional/excess return per unit of downside negative risk.
-Focuses on only negative fluctuations rather than total risk.
-ST = Ri - t / DRi or ST = Ri - t / σd
where t is comparision rate, could be RFR and σd is standard deviation of downside risk.
- Jensens alpha + interpretations of value
-Measures how much a portfolio out/underprerforms compared to predictions made by the CAPM.
-Doesnt take into acconunt managers ability to diversify, calculates risk premiums relative to beta/systematic risk.
Rit - Rf = ai + Bi(Rmt - Rf) + Eit
-rearrange for a (Rit = portfolio i return at time t, RM market return etc.)
-If a = 0, port perfroms exactly as predicted by capm. portfolio in equilibrium.
-if a > 0, portfolio outperforms predctions of capm, investor has ‘superior ability’.
-if a < 0, port underperforms predictions of capm, suggesting poor ablity.
With the sortino ratio/measure explain downside risk and a popular measure of it
Measures the volatility of negative returns (below a target, mean return/thresh-hold), unlike standard deviation, which considers both gains and losses.
-Captures what investors consider truely risky.
-Semi deviation is a pop measure, is the sd of only negative returns,
σd = sqrt[1/n * ∑ (Ri - R^)^2 ]
-ri returns if fall belwo the threshold r^, ignore if greater than this threshhold.
-r^ threshold return
-n number returns below the mean/threshold
formula for beta B + special cases
- B = COV (Ri, Rm) / VAR(Rm) =
-ri return of asset, rm market return.
-B = pim * σi / σm
σi = sd of assets returns, σm sd of market returns
beta = 1 mkt beta, The asset’s return moves in line with the market./ same volility as market.
Beta = 0 The asset’s returns are uncorrelated with the market. It does not move with the market at all.
applications of CAPM
-Risk assessment
-Estimating the required return on an investment based on its risk (beta) and the market risk premium.
-Measuring portfolio performance
-Stock evaluation of individual securities or portfolios using metrics like Jensen’s Alpha
-Cost of equity calculation for companies to determine the expected return required by shareholders.
-Capital budgeting to assess the whether an investment should take place based on their risk-adjusted return.
Comparing the SML and the CML
-CML used for efficient portfolios (made up of risky assets and riskless assets) and relates total risk, sd to return, while SML used for individual stocks/portfolios and relates return to systematic risk, beta.
-Inefficient portfolios do not lie on the CML.
-CML used Sd (total risk) as measure of risk where SML uses systematic risk, beta.
In equilibrium, the CML represents the optimal portfolios that balance total risk and return, while the SML reflects the correct pricing of assets based on their systematic risk (beta) and expected return according to the CAPM.
Security market line SML
-SML is a graphical represenation of the CAPM model.shows the relationship between the expected return of a security and its systematic risk (beta), and the pure time value of money measured by RFR.
-SML shows the reward for bearing systematic risk, beta, is the market premium Rm - Rf.
-Plotted in (Beta, Ri) space
Formula for portfolio beta
Bp = ∑ wi* bi, weight of asset i in port, beta of asset i
assumptions of the CAPM
-No taxes, transaction costs and information publicly available.
-Investors rational, utolity maxers, mean variance optimisers.
-Investors can borrow and lend at Rf, due to existence of the riskless asset.
- investors have a one-period investment horizon (they plan to invest for the same time frame).
The market consists of all risky assets, and there is a market portfolio that contains all risky assets weighted by their market value.
define apt + general formula
model which states the expected return of an asset is a function of multiple macroeconomic risk factors, where each factor has a corresponding sensitivity (beta) and risk premium, and any mispricing will be corrected through arbitrage.
-APT does not specify the specific factors—it only states that asset returns are influenced by multiple systematic risk factors.
-APT does not require the market portoflio as a factor.
making it more adaptable but also more complex and requiring empirical estimation
Studies strongly suggest that the CAPM be abandoned and replaced with the APT T/F
-false
. While APT is a more flexible multi-factor model, CAPM remains widely used in finance due to its simplicity and practical applications. Instead of replacing CAPM, APT serves as an alternative approach for asset pricing.
some emprical findings of the capm
-returns tend to have a positive linear relationship with beta, including a beta squared term not much explnatory power.
-inclusion of controls for unsystematic risk doesnt improve model for explaining past returns.
-Security market line less steeply sloped than in theory
-intercept typically greater than theoretical comparison.
Describe roll 1997 critique of the emprical tests of the capm’s validity.
-argue emperical tests of the capm are limited.
-predictions rely on imprerfect market represernations.
-proxy for market port, indicies, fail to incude all tradeable shares and other assets, weak proxy.
-Cannot accurately observe true mkt port so proxy important for validity.
describe Farma and french 1993 critique of validity of capm.
-studied performance of 2k+ stocks (1941-1990) conclude beta alone cannot explain returns over time,
-adding macroeconomic risk factors assosiated with the secuirty such as firm size, value etc may improve predictions between risk and return.
eg) they found small cap stocks earned higher average returns and stocks with higher book to amrket ratio expereinced hiugher average returns.
strengths and limitations of capm
-Simple & Easy to Use – Requires only one factor (market beta) for asset pricing.
-Clear Theoretical Foundation – Based on well-defined risk-return trade-off.
-emphasises likely impact systematic risk has on expected returns.
-Widely Used in Practice
-ves:
-Unrealistic Assumptions – Assumes a risk-free rate, no transaction costs, and rational investors.
Single Risk Factor – Only considers market risk, ignoring other factors like size, value, and momentum. providing additional factors may better help explain returns
describe estimating the apt + results of estimating both apt and capm
- Identify macroeconomic risk factors
- using historical data estimate the risk premiums lamda i assosiated with each risk factor.
- using historical data estimate the factor sensitivities betai, finding out how sensitibe the securities returns are to the respective factor.
- calculate the expected return using the estimated apt model
-both models yield similar results for some industries, oil gas) however large differences in others (machinery)
-Both models express the importance of divresidfication for reducing un systeamtic rislk.
