Portfolio Management
treynor measure calculation
(Rp - Rf) / ßp, interpreted as excess returns per unit of systematic risk, ad represented by the slope of a line.
two issues of active portfolio management
1) an investor may have multiple managers actively managing to the same benchmark for the same asset class. some may over weight some under weight. taken together, there is no net active management risk although each manager has reported active management risk. overall, the risk budget is underutilized as there is less net active management than gross active management 2) when all managers are actively managing portfolios relative to an index, trading may be excessive overall. this extra trading could have negative tax consequences, specifically potentially higher capital gains taxes, compared to an overall efficient tax strategy
assumptions of CAPM
1) risk aversion (to accept a greater degree of risk, investors require a higher exited return 2) utility maximizing investors (investors choose the portfolio, based on their individual preferences, with the risk and return combination that maximizes their expected utility 3)frictionless markets (there are no taxes, transaction costs, or other impediments to trading 4)one period horizon (all investors have the same one period time horizon 5)homogenous expectations (all investors have the same expectations for assets' expected returns, st. dev. of returns and returns correlations between assets 6)divisible assets (infinitely divisible) 7)competitive markets (investors take the market price as given and no investor can influence prices with their trades)
major components of the IPS
1)description of client (investment objectives, situation, circumstances) 2) statement of the purpose of the IPS 3)statement of duties and responsibilities of investment manager, custodian or assets, and the client 4)procedures to update the IPS and to respond to various possible situations 5)investment objectives 6)investment constraints 7)investment guidelines. 8)evaluation of performance 9)appendices. in any case, the IPS will at a minus contain a clear statement of client circumstances and constraints, an investment strategy based on these, and some benchmark against which to evaluate the account performance
jensen's alpha equation
= Rp - [Rf + ßp(Rm - Rf)] and is the percentage portfolio return above that of a portfolio or security with the same beta as the portfolio that lies on the SML.
total risk (as measured by st. dev.)
= systematic risk + unsystematic risk
Stock A has a standard deviation of 4.1% and Stock B has a standard deviation of 5.8%. If the stocks are perfectly positively correlated, which portfolio weights minimize the portfolio's standard deviation?
Because there is a perfectly positive correlation, there is no benefit to diversification. Therefore, the investor should put all his money into Stock A (with the lowest standard deviation) to minimize the risk (standard deviation) of the portfolio.
example using beta to estimate required return
Company has a capital structure that is 40% debt and 60% equity. the expected return on the market is 12% and the risk free rate is 4%. what discount rate should an analyst use to calculate the NPV of a project with an equity beta of 0.9 if the firm's after-tax cost of debt is 5%.? required return on equity is .04 + .9(.12 - .04) = 11.2% discount rate = .4(5%) + .6(11.2%) = 8.72%
single index / single factor model
E(Ri) - Rf = ßi x [E(Rm) - Rf] the expected excess return (return above Rf) is the product of the factor weight/sensitivity, ßi, and the risk factor, which in this model is the excess return on the market portfolio or market index.
general form of a multi factor model
E(Ri) - Rf = ßi1 x E(Factor 1) + ßi2 x E(Factor 2) + ... + ßik x E(Factor k) this model states that the expected excess return above the Rf for Asset i is the same of each factor sensitivity or factor loading (the ßs) for Asset i multiplied by the expected value of that factor for the period.
SML equation
E(Ri) = RFR + [(E(Rmkt) - RFR)/Om^2 ] x COVi,mkt = E(Ri) = RFR + [COVi,mkt / Om^2 ] x [E(Rmkt) - RFR] this second equation is the most common means of deescribing the SML, and this relation between beta (systematic risk) and expected return is known as the Capital Asset Pricing Model. it is a graphical representation of the CAPM
expected return on portfolio / portfolio st. dev. with Rf
E(Rp) = (1 - Wm) x Rf + Wm x E(Rm) Op = Wm x Om
do you have to buy all stocks in the market to diversify away unsystematic risk?
No. academic studies have shown that as you increase the number of stocks in a portfolio, the portfolio's risk falls toward the market risk. one study showed that it only took about 12 to 18 stocks in a portfolio to achieve 90% of the maximum diversification possible. Whatever the number , IT IS SIGNIFICANTLY LESS THAN ALL THE SECURITIES
proxy statements
Proxy statements are issued to shareholders when there are matters that require a shareholder vote. These statements, which are also filed with the SEC and available from EDGAR, are a good source of information about the election of (and qualifications of) board members, compensation, management qualifications, and the issuance of stock options.
important points to cover in IPS
R-R-T-T-L-L-U. risk , return, time horizon , tax situation, liquidity , legal restrictions, and unique constraints
market model equations
Ri = Ai + ßiRm + Ei Ri = return on asset i Rm = market return ßi = slope coefficient (estimated from historical return data) Ai = intercept (estimated from historical return data) Ei = abnormal return on Asset i we can require that Ai is the risk free rate times (1-ßi) to be consistent with the general form of a single index model in excess returns form.
three steps in portfolio management process
The three major steps in the portfolio management process are (1) planning, (2) execution, and (3) feedback. The planning step includes evaluating the investor's needs and preparing an investment policy statement. The execution step includes choosing a target asset allocation, evaluating potential investments based on top-down or bottom-up analysis, and constructing the portfolio. The feedback step includes measuring and reporting performance and monitoring and rebalancing the portfolio.
variance of portfolio
W1^2xVariance1 + W2^2xVariance2 + 2W1W2Cov1,2 = W1^2xVariance1 + W2^2xVariance2 + 2W1W2p1,2o1o2
how to interpret correlation coefficient
a correlation coefficient of +1 means that deviations from the mean or expected return are always proportional in the same direction. that is, they are perfectly positively correlated -1 means that the deviations from the mean or expected return are always proportional in opposite directions 0 means that there is no liner relationship between the two stocks' returns. knowing the actual value of one variable tells you nothing about the value of the other.
Fama and French
a multifactor model. they estimated the sensitivity of security returns to three factors: firm size, firm book value to market value ratio, and the return on the market portfolio minus the Rf. Earhart suggests a fourth factor that measures price momentum using prior period returns. together, these four factors do a relatively good job of explaining returns differences for US equities over the period for which the model has been estimated.
core-satellite approach
addresses those issues by investing the core/majority of the portfolio in passively managed indexes and invests a smaller or satellite portion in active strategies. this approach reduces the likelihood of excessive trading and offsetting active positions.
points along CML
all points on the CML (except the tangency point) represent the risk return characteristics of portfolios formed by either combining the market portfolio with the risk-free asset or borrowing at the Rf in order to invest more than 100% of the net value. tangency on the CML represents the market expected return. PORTFOLIOS THAT DO NOT LIE ON THE CML ARE NOT EFFICIENT AND THEREFORE HAVE RISK THAT WILL NOT BE REWARDED WITH HIGHER EXPECTED RETURNS IN EQUILIBRIUM
cont. 3
an established manufacturer of machine tools may not be a very risky investment in terms of total risk, but may have a greater sensitivity to market risk factors than he biotech stock. given this scenario, the stock with more total risk (biotech) has less systematic risk and will therefore have a lower equilibrium rate of return according to capital market theory.
population variance / same variance
are the same as in statistics. use T -1 in denominator for sample variance.
return generating models
are used to estimate the expected returns on risky securities based on specific factors. for each security, we must estimate the sensitivity of its returns to each specific factor. factors that explain security returns can be classified as macroeconomic, fundamental, and statistical factors. however, statistical factors may not have any theoretical basis, so analysts prefer the other two.
adding a risk free asset into a risky portoflio
because a risk free asset has zero standard deviation and zero correlation of returns with those of a risky portfolio, this results in the reduced equation: Oportfolio = (Wa^2 x Oa^2)^1/2 = Wa x Oa
tax situation
besides an individual's overall tax rate, the tax treatment of various types of investment accounts is also a consideration in portfolio construction. for a full taxable account, investors subject to higher tax rates may prefer tax-free bonds to taxable bonds or prefer equities that are expected to produce capital gains. a focus on expected after tax returns over time in relation to risk should correctly account for differences in tax treatments as well as investor's overall tax rates.
two fund separation theorem
combining a risky portfolio with a risk free asset, which states that all investor's optimum portfolios will be made up of some combination of an optimal portfolio of risky assets and the risk free asset.
ability to bear risk
depends on financial circumstances. longer investment horizons , greater wealth, and more insurance against unexpected occurrences, and a secure job all suggest a greater ability to bear investment risk in terms of uncertainty about periodic investment performance.
unique circumstances
each investor whether individual or institutional may have specific preferences or restrictions on which securities and assets may be purchases for the account. ethical preferences such as tobacco or firearm are not uncommon. religious objections, human rights, etc.
Holding period return
end of period value (including dividends) / beginning of period value
note of caution
estimating the values needed to apply these theoretical models and performance measures is often difficult and is done with error. the expected return on the market, and thus the market risk premium, may not be equal to its average historical value. estimating security and portfolio betas is done with error as well.
minium variance portfolios / minimum variance frontier
for each level of expected portfolio return, we can vary the portfolio weights on the individual assets to determine the portfolio that has the least risk. these portfolios that have the lowest standard deviation of all portfolios with a given expected returns are known as minimum variance portfolios and together make up the minimum variance frontier
security market line
given that the only relevant (priced) risk for an individual asset i is measured by the covariance between the asset's returns and the returns on the market, COVi,mkt, we can plot the relationship between risk and return for individual assets using COVi,mkt as our measure of systematic risk. the resulting line is one version of what is referred to as the SML
portfolios that lie above CML/SML...
have sharpe ratios greater than those of any portfolios along the CML and have positive m2 measures. Portfolios that lie above the SML have Treynor measures greater than those of any security or portfolio that lies along the SML and also have positive values for Jensen's alpha.
using jensen's alpha vs sharpe vs m2 vs treynor measure
if a single manager is used, then the total risk including any nonsystematic risk is the relevant measure and risk adjustment using total risk, as with the sharpe and M2 measures, is appropriate. if a fund uses multiple managers so that the overall fund portfolio is well diversified ( no systematic risk) , then the performance measures based on systematic risk (beta), such as the Treynor measure and Jensen's alpha , are appropriate.
how to determine is stock is over/under/correctly valued
if the forecasted return (using beginning and ending prices + dividends) is LESS than the required return (using CAPM), the stock is OVERVALUED. it plots below SML if the forecasted return is GREATER THAN required return, the stock is UNDERVALUED. it plots above SML if its properly valued (required = forecasted), it plots ON SML. ALL STOCKS SHOULD PLOT ON THE SML UNLESS THEY ARE MISPRICED
time horizon
in general, the longer an investor's time horizon, the more risk and less liquidity the investor can accept in the portfolio.
investment constraints
include the investor's liquidity needs, time horizon, tax considerations, legal and regulatory constraints, and unique needs
indifference curves cont.
indifference curves slope upward for risk-averse investors because they will only take on more risk (st. dev.) if they are compensated with greater expected returns. an investor who is relatively more risk averse requires a relatively greater increase in expected return to compensate for a given increase in risk. in other words, A MORE (LESS) RISK AVERSE INVESTOR WILL HAVE STEEPER (FLATTER) INDIFFERENCE CURVES, REFLECTING A HIGHER RISK AVERSION COEFFICIENT
passive investment strategy
investors who believe market prices are informationally efficient often follow a passive investment strategy (i.e., invest in an index of risky assets that serves as a proxy for the market portfolio and allocate a portion of their investable assets to a risk free asset)
expected return on asset i
is Ai + ßiE(Rm) a deviation from the expected return in a given period is the abnormal return on Asset i, Ei, or: Ri - (Ai + ßiRm) in the market model , the factor sensitivity or beta for Asset i is a measure of how sensitive the return on Asset i is to the return on the overall market portfolio
geometric mean return
is a compound annual growth rate. will be less than arithmetic if rates of return vary. [(1+R1)x(1+R2)(1+R3)...]^1/N - 1
willingness to bear risk
is based primarily on the investor's attitutes and beliefs about investments. the assessment of an investor's attitude about risk is quite subjective and is sometimes done with a short questionnaire
strategic asset allocation
is developed which specifies the percentage allocations to the included asset classes. the correlation of returns WITHIN an asset class should be relatively high, indicating that the assets within the class are similar in their investment performance. it is LOW CORRELATIONS of returns BETWEEN asset classes that leads to risk reduction through portfolio diversification. the asset allocation for the efficient portfolio selected is then the strategic asset allocation for the portfolio.
real return
is nominal return adjusted for inflation. consider an investor who earns a nominal return of 7% over a year when inflation is 2%. the investor's approximate real return is simpy 7 - 2 = 5%. the investor's exact real true is 1.07 / 1.02 = 4.9%. real return measures the increase in an investor's purchasing power.
risk averse investor
is simply one that dislikes risk. given two investments that have equal expected returns, a risk averse investor will choose the one with less risk (smaller st. dev.) however, an investor may select a very risky portfolio despite being risk averse; a risk averse investor will hold very risky assets if he feels that the extra return he expects to earn is adequate compensation for the additional risk.
important conclusion of capital market theory
is that equilibrium security returns depend on a stock's or a portfolio's systematic risk, not its total risk as measured by standard deviation. one of the assumptions of the model is that diversification is free. the reasoning is that investors will not be compensated for bearing risk that can be eliminated at no cost. if you think about the costs of a no-load index fund compared to buying individual stocks, diversification si actually very low cost if not actually free.
simplifying assumption underlying modern portfolio theory and CAPM
is that investors have homogenous expectations ( i.e. y they all have the same estimates of risk, return, and correlations with other risky assets for all risky assets) UNDER THIS ASSUMPTION, ALL INVESTORS FACE THE SAME EFFICIENT FRONTIER OF RISKY PORTFOLIOS AND WILL ALL HAVE THE SAME OPTIMAL RISKY PORTFOLIO AND CAL.
tracking error
is the difference between the total return on a portfolio and the total return on the benchmark used to measure the portfolio's performance
arithmetic mean return
is the simple average of a series of periodic returns. it has the statsitical property of being an unbiased estimator of the true mean of the underlying distributions of returns
active portfolio management
many investors and portfolio managers believe their estimates of security values are correct and market prices are incorrect. such investors will not use the weights of the market portfolio but will invest more than the market weights in securities that they believe are undervalued and less than the market weights that are overvalued.
overpriced stock
means that the expected return is too low given its systematic risk. BECAUSE THE EQUATION OF THE SML IS THE CAPM, YOU CAN DETERMINE IF A STOCK IS OVER OR UNDER VALUED GRAPHICALLY OR MATHEMATICALLY.
covariance
measures the extent to which two variables move together over time. a positive covariance means that the variables tend to move together. negative covariance means they move in opposite directions. a covariance of zero means there is no linear relationship between the two variables.
absolute risk objectives
might be to "have no decrease in portfolio value during any 12 month period" or to "not decrease in value by more than 2% at any point over any 12 month period". can also be stated in terms of the probability of specific portfolio results, either % losses or dollar losses: "no greater than a 5% probability of returns below -5% in any 12 month period". can be stated in nominal or real terms
multifactors models
most commonly use macroeconomic factors such as GDP growth, inflation, or consumer confidence, along with fundamental factors such as earnings, earnings growth, firm size, and research expenditures. statistical factors often have no basis in fiannce theory and are suspect in that they may represent only relations for a specific time period which have been repeated by data mining
correlation coefficient
p1,2.... the correlation coefficient has no units. it is a pure measures of the co movement of the two stock's returns and is bounded by -1 and +1
indifference curve
plots combinations of risk (st. dev.) and expected return among which an investor is indifferent. in constructing indifference curves for portfolios based on only their expected return and st. dev. of return, we are assuming that these are the only portfolio characteristics hat investors care about.
M squared measured
produces the same portfolio rankings as the Sharpe Ratio but is stated in percentage terms = (Rp - Rf) x Om/Op - (Rm - Rf) the intuition of this measure is that the first term is the excess return on portfolio P*, constructed by taking a leveraged position in Portfolio P so that P* has the same total risk, Om, as the market portfolio. the excess return on such a leveraged portfolio is greater than the return on the market portfolio by the vertical distance M^2
leveraged return
refers to a return to an investor that is a multiple of the return on the underlying asset. the leveraged return is calculated as the gain or loss on the investment as a percentage of an investor's cash investment. an investment in a derivative security, such as a futures contract, produces a leveraged return because the cash deposited is only a fraction of the value of the assets undlerying the futures contract. very common in real estate.
tactical asset allocation
refers to an allocation that deviates from the baseline (Strategic) allocation in order to profit from a forecast of shorter-term opportunities in specific asset classes.
security selection
refers to deviations from index weights on individual securities within an asset class. i.e. overweight energy, underweight tech, etc.
liquidity
refers to the ability to turn investment assets into spendable cash in a short period of time without having to make significant price concessions to do so.
net return
refers to the return after these fees have been deducted. (commissions on trades are deducted)
pre tax nominal return
refers to the return prior to paying taxes. dividend income, interest income, short term capital gains, and long term capital gains may all be taxed at different rates
gross return
refers to the total return on a security portfolio before deducting fees for the management and administration of the investment account (commissions on trades are deducted)
relative risk objectives
relate to a specific benchmark and can also be strict, such as, "Returns will not be less than 12-month euro LIBOR over any 12 month period" or "No greater than a 5% probability of returns more than 4% below the return on the MSCI World Index over any 12 month period.
investor's utility function
represents the investor's preferences in terms of risk and return. (i.e. his degree of risk aversion)
after tax nominal return
return after tax liability is deducted.
risk budgeting
sets an overall risk limit for the portfolio and budgets (allocates) a portion of the permitted risk to the systematic risk of the strategic asset allocation, the risk from tactical asset allocation, and the risk from security selection
market model
simplified version of a single index model which us used to estimate a security or portfolio's beta and to estimated a security's abnormal return (return above expected return) based on the actual market return
security characteristic line
slope of the SCL is COVim/Om^2, which is the same formula we used to calculate beta
characteristics of the major asset classes that investors consider in forming portfolios
small cap stocks have had the greatest average returns and greatest risk over the period. t - bills had the lowest average returns and the lowest standard deviation of returns. evaluating investments using expected return and variance of returns is a simplification because returns do not follow a normal distribution; distributions are negatively skewed with greater kurtosis (fatter tails) than a normal distribution. this negative skew reflects a tendency towards large downside deviations, whole the positive excess kurtosis reflects frequent extreme deviations on both the upside and downside.
defining beta
so, we can define beta, ß = COVi,mkt / Om^2, as a standardized measure of systematic risk. beta measures the relation between a security's excess returns and the excess return to the market portfolio.
sample covariance
sum of [(Rt,1 - R1)(Rt,2 - R2)] / n - 1 Rt,1 = return on Asset 1 in period t Rt,2 = return on Asset 2 in period t R1 = mean return on asset 1 R2 = mean return on asset 2 n = number of periods is an absolute measure and is measured in return units squared
CML vs SML
the CML uses total risk = Op on the x - axis. hence, only efficient portfolios will plot on the CML. on the other hand, the SML uses beta (systematic risk) on the x-axis. so in a CAPM world, ALL PROPERLY PRICED SECURITIES AND PORTFOLIOS OF SECURITIES WILL PLOT ON THE SML
SML cont.
the SML shows the equilibrium (required) return for any security or portfolio based on its beta (systematic risk)
examples of systematic risk
the concept of systematic risk applies to individual securities as well as portfolios. some securities' returns are highly correlated with overall market returns such as Ferrari and Harley Davidson. these firms have high systematic risk (i.e. they are very responsive to market , or systematic, changes) Other firms , such as utility companies, respond very little to changes in the systematic risk factors.
correlation
the covariance of the return of two securities can be standardized by dividing by the product of the standard deviations of the two securities. p1,2 = Cov1,2 / o1o2 Cov1,2 = p1,2 x o1 x o2
market risk premium
the difference between the expected return on the market and the risk-free rate. Using E(Rp) = Rf + (E(Rm) - Rf)(Op/Om) , we can see that an investor can expect to get one unit of market risk premium in additional return (above the risk free rate) for every unit of market risk, Om, that the investor is willing to accept. if we assume that investors can both lend (invest at the Rf) and borrow (as with a margin account) at the Rf, they can select portfolios to the right of the market portfolio.
according to the CAPM
the expected returns on all portfolios, well diversified or not, are determined by their systematic risk. NOTE THAT A LOW BETA STOCK IS NOT NECESSARILY LOW-RISK WHEN TOTAL RISK IS CONSIDERED. IT MAY HAVE QUITE LOW SYSTEMATIC RISK IF THE UNCERTAINTY ABOUT ITS FUTURE RETURNS DEPENDS PRIMARILY ON FIRM SPECIFIC FACTORS. FURTHER, ALL SECURITIES AND PORTFOLIOS, DIVERSIFIED OR NOT, WILL PLOT ON THE SML IN EQUILIBRIUM. in fact, all stocks and portfolios with a beta of 1 will plot at the same point on the SML regardless of total risk
important thing to remember about what the correlation is
the greatest portfolio risk results when the correlation between asset returns is +1. for any value of correlation less than +1, portfolio variance is reduced. note that for a correlation of zero. the entire third term in the portfolio variance equation is zero. for negative values of correlation p12, the third term becomes negative and further reduces portfolio variance and st. dev. THE LOWER THE CORRELATION OF ASSET RETURNS, THE GREATER RISK REDUCTION (DIVERSIFICATION) BENEFIT OF COMBINING ASSETS IN A PORTFOLIO. If asset returns were perfectly negatively correlated, portfolio risk could be eliminated altogether for a specific set of asset weights.
cont. 2
the high risk of our biotech, however, is primarily from firm specific factors, so its unsystematic risk is high. because market facts such as economic growth rates have little to do with the eventual outcome for this stock, systemic risk is a small proportion of the total risk of the stock. capital market theory says that the equilibrium return on this stock may be less than that of a stock with much less firm specific risk but more sensitivity to the factors that drive the return of the overall market.
cont.
the implications of this conclusion are very important to asset pricing (expected concerns). the riskiest stock, with risk measured as st. dev. of returns, does not necessarily have the greatest expected return. consider a biotech stock with one new drug product that is in clinical trials to determine its effectiveness. if it turns out that the drug is effective and safe, stock returns will be quite high. if, on the other hand, the subjects in the clinical trials are killed, the stock will fall to approximately zero and returns will be quite poor. this describes a stock with high st. dev. of returns.
capital allocation line
the line representing these possible combinations of risk free assets and the optimal risky asset portfolio. the best CAL is the one that offers the most preferred set of possible portfolios in terms of their risk and return.
under the homogenous assumption...
the optimal CAL for any investor is the one that is just tangent to the efficient frontier. depending on their preferences for risk and return (indifference curves) investors may choose different portfolio weights fro the risk free asset and the risk (tangency) portfolio. every investor will use the same risky portfolio. when this is the case, THAT PORTFOLIO MUST BE THE MARKET PORTFOLIO OF ALL RISKY ASSETS BECAUSE ALL INVESTORS THAT HOLD ANY RISKY ASSETS HOLD THE SAME PORTFOLIO OF RISKY ASSETS
global minimum variance portfolio
the portfolio on the efficient frontier that has the least risk
efficient frontier
the portfolios that have the greatest expected return for each level of risk. the efficient frontier coincides with the top portion of the minimum variance frontier. a risk averse investor would only choose portfolios that are on the efficient frontier because all available portfolios that are not on the efficient frontier have lower expected returns that an efficient portfolio with the same risk
unsystematic risk
the risk that is eliminated by diversification. because the market portfolio contains all risky assets, it must be a well diversified portfolio. all the risk that can be diversified away has been.
systematic risk
the risk that remains that cannot be diversified away
beta
the sensitivity of an asset's return to the return on the market index in the context of the market model. it is a standerdized measure of the covariance of the asset's return with the market return. ßi = covariance of Asset i's return with the market return / variance of the market return = COVim / O^2m substituting for COVim we can also calculate beta as: ßi = (PimOiOm) / Om^2 = Pim x (Oi/Om)
sharpe ratio cont.
the sharpe ratio is the slope of the CAL for the portfolio and can be compared to the slope of the CML, which is the sharpe ratio for any portfolio along the CML.
tracing risk
the standard deviation of the difference between a portfolio return and an index (or any chosen benchmark return)
peer performance benchmarks suffer from not being investable portfolios
there is no way to match this investment return by portfolio construction before the fact.
legal and regulatory
trust , corporate, and qualified investment accounts may all be restricted by law from investing in particular types of securities and assets. there may also be restrictions on percentage allocations to specific types of investments in such accounts.
treynor measure and jensen's alpha
two measures of risk adjusted returns based on systematic risk (beta) rather than total risk. they are similar to the sharpe ratio and M2 in that the Treynor measure is based on slope and Jensen's alpha is a measure of percentage returns in excess of those from a portfolio that has the same beta but lies on the SML.
capital market line
under the assumption of homogenous expectations, this optimal CAL for all investors is terms the CAPITAL MARKET LINE (CML). along this line, expected portfolio return, E(Rp), is a linear function of portfolio risk, Op. the equation of the line is: E(Rp) = Rf + [(E(Rm) - Rf) / Om]xOp = E(Rp) = Rf + (E(Rm) - Rf)(Op/Om) the Y - intercept of this line is Rf and the slope is (E(Rm) - Rf) / Om] plots return against TOTAL RISK which is measured by st. dev. of returns
summing up.
unsystematic risk is not compensated in equilibrium because it can be eliminated for free through diversification. systematic risk is measured by the contribution of a security to the risk of a well diversified portfolio, and the expected equilibrium return (required return) on an individual security will depend only on it systemic risk.
if two risky asset returns are perfectly positively correlated, p1,2 = +1, then the square root of portfolio variance (St. dev.) is equal to
w1o1 + w2o2
sharpe ratio
when we evaluate the performance of a portfolio with risk that differs from that of a benchmark, we need to adjust the portfolio returns for the risk of the portfolio. the sharpe ratio of a portfolio, [ (Rp - Rf) / Op] , is its EXCESS RETURNS PER UNIT OF TOTAL PORTFOLIO RISK., and higher sharpe ratios indicate better risk adjusted portfolio performance. note that this is a slop measure and the sharpe ratio of all portfolios along the CML are the same. because the ratio uses total risk, rather than systematic risk, it accounts for any unsystematic risk that the portfolio manager has taken. it is only useful when comparing it with another portfolio's sharpe ratio.
