Finance 302 Chapter 8 Risk and Return

financial portfolio

1.A listing of all the investments that a person holds 2.one's total investment

Beta and Diversified Portfolio

1.Average Beta=1.0 and is Market Beta 2.Beta <1.0=Less Risky than the market like Utility Stocks 3.Beta>10=More Risky than the Market like High Tech Stocks 4.Beta=0 is Independent of the Market like a Treasury Bill 5.Beta are estimated by running a regression line of stock returns against market returns(Independent Variable) 6.The slope of the Regression Line (Coefficient of the Independent Variable) measures Beta or the Systematic Risk Estimate of the Stock 7.Once Individual Stock Betas are determined the Portfolio Beta is easily calculated as the Weighted Average. 8.Formula on the formula sheet

Extrapolating Holding Period Returns

1.Extrapolating short-term HPRs into APRs and EARs is mathematically correct, but often unrealistic and infeasible. 2.Implies earning the same periodic rate over and over again in 1 year. 3.A short holding period with fairly high HPR would lead to huge numbers if return is extrapolated.

The Risk and Return Tradeoff

1.Investment Rule number 1: if faced with two investment choices having the same expected returns, select the one with the lower expected risk 2.Investment Rule number 2: if two investment choices have similar risk profiles, select the one with the higher expected return 3.if you want a higher return you must take on a higher risk, hence the risk/return tradeoff 4.historically higher expected returns are accompanied by greater variances thus greater standard deviations 5.the investor's tolerance for risk and attitude towards risk matters 6.Diversification is the key

The Security Market Line

1.It shows the relationship between an asset's required rate of return and its systematic risk measure which is Beta 2.It is based on 3 assumptions: (A)there is a basic reward for waiting:risk free rate (B)Investors expect to e proportionately compensated for bearing risk (C)there is a consistent tradeoff between risk and reward. As risk doubles, so does the required rate of return, and vice-versa 3.These assumptions imply that the SML is upward sloping 4.it also has a constant linear slope 5.it has the risk-free rate as the Y-intercept

Two different measures of risk related to Financial Assets

1.Standard Deviation: measures the total risk of an asset. (A).It measures ts systematic risk and its unsystematic risk (B)If we do not have a Well-diversified Portfolio it is better to use Standard Deviation 2.Beta-measure of an asset's systematic risk (A)If an asset is a part of a well-diversified portfolio

Diversification: Minimizing Risk or Uncertainty

1.by dividing up one's investments across many relatively low-correlated assets, companies, industries, and countries, it is possible to considerably reduce one's exposure to risk 2.Henry Marowitz 1955 "Portfolio Selection" Journal of Finance 3.birth of the Modern Quantitative Financial Movement

returns in an uncertain world

1.for future investments we need expected or ex-ante rather than ex-post return and risk measures 2.for ex ante measures we need probability distributions and then the expected return and risk measures are estimated using the equations for: (A1)Expected value or Expected payoff (B2)standard deviation (C) they are on the formula sheet

Risk (Certainty and Uncertainty)

1.future performance of most investments is uncertain 2.risky implies not only the potential for loss but also for uncertain gain 3.risk does not take sides 4.it is important to measure and analyze the risk potential of an investment, so as to make an informed decision 5.a lot more risk historically speaking with small company stocks

how do we measure return

1.holding period return (HPR)also the cumulative rate of return 2.rate(HPR)=W(end)+Distributions-W(beginning)/W(beginning) 3.rate(HPR)=P(end)+Distributions-P(beginning)/P(beginning) (3A) where P=Price 4.also:P(end)+Distributions/P(beginning)-1

normal distributions

1.if we assume that a variable is normally distributed then... (A)a normal distribution has a mean=0 and a standard deviation=1 (B)about 68% of the area lies within 1 standard deviation from the mean (C)about 95% of the observations lie within 2 standard deviations from the mean (D)about 99% of the observations lie within 3 standard deviations from the mean (E)smaller variances are less risky investments (F)less risky investments equals less uncertainty about their future performance

Beta

1.measures is a statistical measure of the volatility of an individual security compared with the market as a whole 2.it is the relative tendency of a security's return to respond to overall market fluctuations

Diversification benefit

1.must combine stocks that are not perfectly positively correlated with each other 2.increase the negative correlation between two stocks, increase the reduction in risk achieved by adding it to the portfolio

unsystematic risk/Diversifiable Risk

1.sometimes called idiosyncratic risk 2.related to asset(company) specific 3.events/uncertainty (product or labor problems) 4.firm-specific or industry-specific 5.can eliminate it when we spread other investments over different stocks

systematic risk/Nondiversifiable Risk

1.sometimes called market risk 2.recession or inflation 3.affected by the uncertainty of future economic conditions that affect all stocks (companies) that operate in the economy 4.we cannot eliminate it as we spread our investments

variance

1.standard deviation squared 2.measures the statistical dispersion by finding the average squared difference between the actual observations (like individual heights of students) and the average observation (average class height) 3.the larger the variance the greater the dispersion 4.we take the sum of: the payoff of the return minus the Expected return and square it. then multiply it by the probability of the outcome occurring

The Capital Asset Pricing Model

1.the equation of the SML showing the relationship between expected return and beta(systematic risk) 2.It states that the expected return of an investment is a function of: (A)The time value of money(the reward for waiting) (B)A reward for taking on risk (C)The amount of risk 3.the formal equation for the SML (Security Market Line)is the CAPM (Capital Asset Pricing Model) 4.The slope of the SML (Security Market Line) is the market risk premium and not Beta

two factors that affect risk

1.the range of possible outcomes 2.the tendency or lack of tendency of the returns to bunch together near the mean or average

standard deviation

1.the square root of the variance and provides a measure of the standard, or average, distance from the mean (dispersion) 2.it measures the volatility of an investment 3.the higher a security's volatility the more a return fluctuates over time 4.used to calculate the risk of n investment where 'i' is the individual payoff and matching probability of that particular outcome

Expected Payoff (Value)

1.to find the expected payoff we take the sum of the probability of each possible return outcome (probability of 'i') and multiply it by the payoff outcome itself (payoff of 'i') 2.where the subscript 'i' on each payoff and probability is the individual potential outcome and the matching probability that we associate with that particular outcome 3.the forward looking measure of a return 4.effectively a weighted average of the outcomes 5.where 'X' of 'i' is observation 'i' (return) and 'p' of 'i' is the respective probability of that observation (return) occurring

Diversification:Types of Risks

1.unsystematic or diversifiable risk 2.systematic or non-diversifiable risk 3.well-diversified portfolio

Variance and Standard Deviation

1.variance and standard deviation are measures of dispersion 2.helps researchers determine how spread out or clustered together a set of numbers or outcomes is around their mean or average value. 3.the larger the variance the greater is the variability, hence the riskiness of a set of values

Holding period to Annual return

1.with varying holding periods, holding period returns not good for comparison 2.Simple annual return: APR=HPR/n 3.Effective Annual rate of return: EAR=[(1+HPR)^1/n] -1 4.where 'n' is the number of years or proportion of a year that the holding period consists of

well-diversified portfolio

A portfolio that has essentially eliminated all unsystematic risk.

ex post

After the fact or event in question has occurred.

ex ante

Before the fact or event in question has occurred.

risk

a measure of the uncertainty in a set of potential outcomes for an event in which there is a chance of some loss

uncertainty

absence of knowledge of the actual outcome of an event before it happens

Comparing HPR's

example:Given Joe's HPR of 20% over 4 months and Jane's HPR of 25% over 2 years, is it correct to conclude that Jane's investment performance was better than that of Joe? 1.Joe's holding period (n)=4/12=1/3 year=.333 years Joe's APR=HPR/n=20%/.333=60% Joe' EAR=[(1+HPR)^1/n] -1 [(1.20)^1/.333] -1=73.76% 2.Jane's holding period (n)= 2 years Jane's APR=HPR/n=25%/2=12.5% Jane's EAR=[(1+HPR)^1/n] -1 [(1.25)^1/2] -1=11.8% 3.Clearly on an annual basis Joe's investment far outperformed Jane's investment

calculating dollar and percentage returns

example:Joe bought some gold coins for $1000 and sold them 4 months later for $1200. Jane on the other hand bought 100 shares of stock for $10 and sold those 2 years later for $12 per share after receiving $0.50 per share as dividends for the year. Calculate the dollar profit and percent return earned by each investor over their respective holding periods. 1.Joe's Dollar Profit=Ending value -Original cost $1200-$1000=$200 2.Joe's HPR=Dollar profit/Original Cost $200/$1000=20% 1.Jane's Dollar Profit=Ending value+Distributions-Original cost ($12)(100 shares)+($0.50)(100 shares)-($10)(100 shares)=$250 2.Jane's HPR=$250/$1000=25%

assessing market attractiveness

example:let's say that you are looking into investing into two stocks, A and B. Stock A has a beta of 1.3 and based on your best estimates is expected to have a return of 15% Stock B has a beta of 0.9 and is expected to earn 9%. If the risk-free rate is currently 4% and the expected return on the market is 11%, determine whether these stocks are worth investing in. 1.Stock A expected return=4%+(11%-4%)*1.3=13.1%(what I require in order to make an investment in stock A) 2.Stock B expected return=4%+(11%-4%)*0.9=10.3%(what I require in order to make an investment in stock B) 3.Stock A would plot above the SML, since 15%>13.1% and would be considered undervalued because I am receiving more than what I require 4.Stock B would pot below the SML, since 9%<10.3% and would be considered overvalued because I am receiving less than what I require 5.Don't buy stock B but do buy Stock A

Unrealistic nature of APR and EAR

example:let's say you buy a 100 shares of stock for $2 per share and sell it a week later for $2.50. Calculate your HPR, APR, and EAR. How realistic are the numbers? 1.N=1/52=0.01923 of a year Profit =$2.50-$2.00=$0.50 2.HPR=$0.50/($2.00)(100 shares)=25% APR=25%/0.01923=1300% or 25%*52 weeks=1300% EAR=[(1+HPR)^52] -1 (100)=[(1.25)^52-1] (100)=10,947,544.25% 3.Highly Profitable

certainty

knowing what is going to happen before it happens

cardinal rule of investing

maximize returns and minimize risks

rates of return

performance analysis of an investment requires investors to measure rates over time

Diversification

the spreading of wealth over a variety of investment opportunities so as to eliminate some risk