Risk and Return - Presentation

RISK AND RETURN

RISK AND RETURN(Important Financial Concepts)OBJECTIVESOBJECTIVESUnderstand the meaning and fundamentals of risk and return

Describe procedures for assessing and measuring risk of a single asset

Understand the risk and return for a portfolio

Risk and return for Capital Asset Pricing Model (CAPM)

Risk and Return FundamentalsDEFINITIONSRisk and Return FundamentalsRisk and Return are two key financial considerations in making important business decisions.

Each financial decision presents certain risk and return characteristics, and the combination can increase or decrease a firms share.

In order to optimize the value of the firm, the right balance between risk and return needs to be achieved.

Question: How to measure risk and return?

Risk and Return FundamentalsDEFINITIONS:

Risk A measure of uncertainty surrounding the return that an investment will earn.

Risk (Financial decision making context) -The chance of financial loss, as measured by the variability of expected returns associated with a given asset. (A decision maker should evaluate an investment by measuring the chance of loss, or risk, and comparing the expected risk to the expected return.)

Return - is a profit on an investment

Rate of Return total gain or loss experienced on an investment over a given period of time.

Risk and Return FundamentalsTOTAL RATE OF RETURN The sum of any cash distribution plus the change in the investment value dividing by the beginning-of-period value. Ct + Pt Pt-1 rt = Pt-1Where: rt = actual, expected or required rate of return during period t Ct = cash (flow) received from the asset investment in the period t-1 to t Pt = price (value) of asset at time t Pt-1 = price (value) of asset at time t-1

Risk and Return FundamentalsTOTAL RATE OF RETURN

The change in investment value plus any cash distributions over a defined time period, dividing by the initial investment value.

Return = (ending value - initial value) + cash distribution initial value

Risk and Return FundamentalsEXAMPLE A

The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?Return = (ending value - initial value) + cash distribution initial valueRisk and Return FundamentalsEXAMPLE A

The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?($9.50 - $10.00 ) + $1.00 $10.00Return = 5%Return =Risk and Return FundamentalsEXAMPLE B

Robin wishes to determine the return on two stocks that she owned during 2009, Apple Inc. and Wal-Mart. At the beginning of the year, Apple stock traded for $ 90.75 per share, and Wal-Mart was valued at $ 55.33. During the year, Apple paid no dividends, but Wal-Mart shareholders received dividends of $ 1.09 per share. At the end of the year , Apple stock was worth $ 210.73 and Wal-Mart sold for $ 52.84.

Apple = [($210.73 $90.75) + $ 0 ] / $ 90.75 = 132.2 %

Wal-Mart = [($52.84 $55.33) + $ 1.09 ] / $ 55.33 = -2.5 %

Risk and Return FundamentalsRISK PREFERENCESRisk and Return FundamentalsRISK PREFERENCES:

Risk Averse (risk aversion)

Risk Neutral (risk indifference)

Risk Seeking (risk preference)

Risk and Return FundamentalsRISK PREFERENCES:

Risk Averse The attitude towards risk in which investors would require an increased return as compensation for an increase in risk.

-A risk-averse investor chooses investments whose returns are more certain. They will not make riskier investment unless it offers a higher expected return.


Risk Neutral The attitude towards risk in which investors choose the investment with the higher return regardless of its risk.

-A risk-neutral investor chooses investments based solely on their expected returns, disregarding the risk. They will always choose the investment with the higher expected return regardless of its risk.


Risk Seeking The attitude towards risk in which investors prefer investments with greater risk even if they have lower expected returns.

-A risk-seeking investor prefers investments with higher risk and may even sacrifice some expected return upon choosing a riskier investment.(i.e. gambling, lottery ticket)


Risk AversionCertainty equivalent (Risk) < Expected return

Risk NeutralCertainty equivalent (Risk) = Expected return

Risk SeekingCertainty equivalent (Risk) > Expected return

NOTE: Most individuals are Risk Averse.

Risk and Return FundamentalsRISK ASSESSMENT

Risk of a Single AssetRISK ASSESMENT:*The more uncertain you are about how an investment will perform, the riskier the investment seems.

SCENARIO ANALYSIS An approach for assessing risk that uses several possible alternative outcomes (scenarios) to obtain a sense of variability among returns.- pessimistic (worst)- most likely (expected)- optimistic (best)

Risk of a Single AssetRISK ASSESMENT:Range A measure of an assets risk, which is found by subtracting the return associated with the pessimistic (worst) outcome from the return associated with the optimistic (best) outcome.Example:

Asset AAsset BInitial Investment$ 10,000$ 10,000Annual Rate of ReturnPessimistic (worst)13%7%Most Likely (expected)15%15%Optimistic (best)17%23%RANGE4% (from 17%-13%)16% (from 23%-7%)Risk of a Single AssetRISK ASSESMENT:

Asset AAsset BInitial Investment$ 10,000$ 10,000Annual Rate of ReturnPessimistic (worst)13%7%Most Likely (expected)15%15%Optimistic (best)17%23%RANGE (best worst)4% (from 17%-13%)16% (from 23%-7%)**The greater the range, the more variability, or risk, the asset is to have.**

Therefore, a risk-averse decision maker would prefer asset A because it offers the same expected (most likely) return with lower risk smaller range.

Risk of a Single AssetRISK ASSESMENT:

PROBABILITY DISTRIBUTION A model that relates probabilities to the associated outcomes.

Probability The chance that a given outcome will occur.100 % - Certain to occur0% - Will never occur(e.g. An outcome with 80 percent probability will be expected to occur 8 out of 10 times)

The simplest type of probability distribution is the bar chart.


Probability OccurrenceAsset AAsset BReturnsValueReturnsValuePessimistic (worst)0.2513%3.257%1.75Most Likely (expected)0.5015%7.5015%7.50Optimistic (best)0.2517%4.2523%5.75TOTAL115.00%15.00%Risk of a Single AssetRISK ASSESMENT:

Note: Although the two assets have the same average return (15 percent), the distribution of returns for asset B is much greater dispersion than the distribution of asset A. Thus, asset B is more risky than asset A


CONTINOUS PROBABILITY DISTRIBUTION A probability distribution showing all the possible outcomes and associated probabilities for a given event.

Expected Rate of ReturnRate ofReturn (%)100150-70Firm XFirm YRisk of a Single AssetRISK MEASUREMENTRisk of a Single AssetRISK MEASUREMENT:

The most common statistical measure to describe an investment risk is its standard deviation.

STANDARD DEVIATION (r) measures the dispersion of an investments return around the expected return.

EXPECTED VALUE OF RETURN () the average return that an investment is expected to produce over time.

Risk of a Single AssetEXPECTED VALUE OF RETURN:

Probability OccurrenceAsset AAsset BReturnsValueReturnsValuePessimistic (worst)0.2513%3.257%1.75Most Likely (expected)0.5015%7.5015%7.50Optimistic (best)0.2517%4.2523%5.75TOTAL115.00%15.00%The expected value of return ( ) for Asset A & B is 15.00%Risk of a Single AssetSTANDARD DEVIATIONRisk of a Single AssetSTANDARD DEVIATION:The standard deviation of a distribution of asset returns is an absolute measure of dispersion of risk about the mean or expected value.

Or just simply, the square root of variance.Risk of a Single AssetSTANDARD DEVIATION:

The standard deviation for Asset A is 1.41%, and the standard deviation for asset B is 5.66%. The higher risk of asset B is clearly reflected in its higher standard deviation.Risk of a Single AssetMORE EXAMPLES FROM OTHER REFERENCE:

Risk of a Single AssetMORE EXAMPLES FROM OTHER REFERENCE:

Risk of a Single AssetMORE EXAMPLES FROM OTHER REFERENCE:

NOTE:A higher standard deviation indicates a greater project risk. With a larger standard deviation, the distribution is more dispersed and the outcomes have a higher variability, resulting in higher risk.Risk of a Single AssetNORMAL PROBABILITY DISTRIBUTIONRisk of a Single AssetNORMAL DISTRIBUTION:It is a symmetrical probability distribution whose shape resembles a bell shaped curve.

Risk of a Single AssetNORMAL DISTRIBUTION:

68 percent of the possible outcomes will lie between +1 to -1 standard deviation from expected value.95 percent of all outcomes will lie between+2 to -2 standard deviation from expected value. 99 percent of all outcomes will lie between+3 to -3 standard deviation from expected value.

Risk of a Single AssetCOEFFICIENT OF VARIATIONRisk of a Single AssetCOEFFICIENT OF VARIATION (CV):

Is a measure of relative dispersion that is useful in comparing risk of assets with differing expected return.

Coefficient Variation = Standard Deviation Expected returnA higher coeficient of variation means that an investment has more volatility relative to its expected return.

For risk averse investors, they may gravitate towards investments with lower coefficient of variation.Risk of a PortfolioPORTFOLIO RETURN AND STANDARD DEVIATIONRisk of a PortfolioPortfolio DefinedIt is a group of financial assets such as stocks, bonds and cash equivalents, as well as their mutual, exchange-traded and closed-fund counterparts.

The goal of financial manager is to create an efficient portfolio.

Efficient Portfolio A portfolio that maximizes return for a given level of risk

Risk of a PortfolioRisk of a PortfolioEXAMPLE:

Stock ValuePurchasedWj= $ value/Total $ value# Shares$ ValueWal-Mart$ 55100$ 5,50068.75%w1= 0.6875Cisco$ 25100$ 2,50031.25%w2= 0.3125TOTAL$ 8,000w1+w2= 1James purchases 100 shares of Wal-Mart at a price of 55 per share, so his total investment in Wal-Mart is $ 5,500. He also buys 100 shares of Cisco Systems at $25 per share, so the total investment in Cisco is $ 2,500. Combining these two holdings, James total portfolio is worth $ 8,000. Of the total, 68.75% is invested in Wal-Mart ($5,500/$8,000) and 31.25% is invested in Cisco Systems ($2,500/$8,000).

Risk of a PortfolioSTANDARD DEVIATION OF A PORTFOLIO RETURN:

This found by applying the formula for the standard deviation of a single asset.

This formula is used when probabilities of the returns are known.This formula is applied when analysts use historical data to estimate the standard deviation.Risk of a PortfolioEXAMPLE:

YearForecasted ReturnPortfolio Return CalculationExp. Retrn.Asset XAsset Y rp = (w1 X r1) + (w2 X r2) + (wn X rn)20138%16%(0.50 X 8%) + (0.50 X 16%)12%201410%14%(0.50 X 10%) + (0.50 X 14%)12%201512%12%(0.50 X 12%) + (0.50 X 12%)12%201614%10%(0.50 X 14%) + (0.50 X 10%)12%201716%8%(0.50 X 16%) + (0.50 X 8%)12%Determining the expected value and standard deviation for portfolio XY, created by combining equal portions (50% each) of assets X and Y. Five years returns of assets forecast on table below. Risk of a PortfolioEXPECTED VALUE OF RETURN:

The expected value of return in a portfolio, when all the outcomes are known and their related probabilities are equal, is a simple arithmetic average as represented by formula below:

The expected value of return in a Single Asset

Risk of a PortfolioEXAMPLE:

By substituting the formula, the expected value of portfolio returns over a 5 year period is 12%.

Risk of a PortfolioEXAMPLE:

The standard deviation is calculated to be 0%. This is because the portfolio return each year is the same (12%).Portfolio returns do not vary through time.Risk of a PortfolioCORRELATION

Correlation is the statistical measure of the relationship between any two series of numbers

Positively correlated Describes two series that move in the same direction.Negatively correlated - Describes two series that move in opposite direction.

Risk of a PortfolioCORRELATION

Correlation Coefficient The measure of the degree of correlation between two series.

Perfectly Positively Correlated Describes two positively correlated series that have a correlation coefficient of +1.

Negatively correlated - Describes two positively correlated series that have a correlation coefficient of -1.

Uncorrelated Describes two series that lack any interaction and therefore have a correlation coefficient close to zero.

Risk of a PortfolioDIVERSIFICATION

Combining negatively, correlated assets to reduce, or diversify risk.

Diversification Reduces RiskBy spreading your portfolio out among several investments, you reduce the total amount committed to any one investment. If you evenly split your portfolio between 5 investments and one goes down the drain, youve still got your other 4 investments to fall back on. If youd put everything in that one bad investment, you would have nothing left.

In this sense, diversification is putting your eggs in different baskets. By not betting everything on one investment, you lessen the risk of losing everything all at once


In general, the lower the correlation between asset returns, the greater the risk that investors can achieve by diversifying.


International DiversificationThe inclusion of assets from countries with business cycles that are not highly correlated with the U.S. Business cycle, reduces the portfolios responsiveness to market movements.

Risk of International Diversification - Currency fluctuations - Political Risk

Risk & Return: CAPM ModelRisk & Return: CAPM ModelCapital Asset Pricing Model (CAPM)The basic theory that links risk and return for all assets.

TYPES OF RISK A. Diversifiable Risk B. Non-diversifiable Risk

Risk & Return: CAPM ModelA. Diversifiable Risk The portion of an assets risk that is attributable to firm-specific, random cause; which can be elimated through diversification. (also called unsystematic risk)

Examples: Strikes, Lawsuits, regulatory actions, change in management, loss of a key account.

B. Non-diversifiable Risk The relevant portion of an assets risk attributable to market factors that affect all firms; cannot be eliminated through diversification. (also called systematic risk)

Examples: War, inflation, overall state of the economy, international incidents, political events.

Risk & Return: CAPM ModelTYPES OF RISK

Risk & Return: CAPM ModelTYPES OF RISK

Risk & Return: CAPM ModelThe Model : CAPMThe capital asset pricing model (CAPM) links nondiversifiable risk to expected returns.

Beta Coefficient is the relative measure of nondiversifiable risk. It is an index of the degree of the degree of movement of an assets return in response to change in the market return.

Market Return The return on the market portfolio of all traded securities.Risk & Return: CAPM ModelDeriving Beta:

The beta coefficient for an asset can be found by plotting the asset's historical returns relative to the returns for the market.

By using statistical techniques, the "characteristic line" is fit to the data points. The slope of this line is beta.

The beta of a portfolio is calculated by finding the weighted average of the betas of the individual component assets.

Deriving Beta:

Risk & Return: CAPM ModelRisk & Return: CAPM ModelDeriving Beta:

Characteristic line is the line of best fit for all the stock returns (Asset returns) relative to Market returns.

The slope of the characteristic line - measures the average relationship between a Asset returns and the Market Returns. This slope (called beta) is a measure of the firms market risk.

Risk & Return: CAPM ModelInterpreting Beta: The beta coefficient for the entire market equals to 1.0. All other betas are viewed in relation to this value.

Risk & Return: CAPM ModelInterpreting Beta:

Risk & Return: CAPM ModelInterpreting Beta:Beta coefficients for actively traded stocks are published in Value Line Investment Survey and in brokerage reports.

Risk & Return: CAPM ModelPortfolio Beta:Indicates the degree of responsiveness of the portfolios return to assets. It is the weighted average of the individual stock betas in the portfolio.

where;wj = proportion of the portfolios dollar value.

Risk & Return: CAPM ModelPortfolio Beta:

Risk & Return: CAPM ModelCAPM Equation:The equation for the Capital Asset Pricing Model is:

Risk & Return: CAPM ModelCAPM Equation:

Risk-free rate of return (RF) The required return on a risk free asset, typically a 3 month US treasury bill.

US Treasury Bill (T-Bills) The required return on a risk free asset, typically a 3 month US treasury bill.

Market risk premium (rm-RF) represents the premium the investor must receive for taking the average amount of risk associated with holding the market.Risk & Return: CAPM ModelCAPM Equation:

INVESTMENTRisk premium(rm-RF) or also (km-RF) Stocks9.3% - 3.9% = 5.4 %Treasury Bond5.0% - 39.% = 1.1Risk premium is higher for stocks than bonds.Risk & Return: CAPM ModelCAPM Equation:

Security Market Line(SML) The depiction of the capital asset pricing model (CAPM) as a graph that reflects the required return in the marketplace for each level of nondiversifiable risk (beta).Risk & Return: CAPM ModelCAPM Equation:

Shifts in Security Market Line Changes in inflationary expectations affect the risk-free rate or returns.

The SML are affected by two major forces:Inflationary ExpectationsRisk Aversion

Changes in Inflationary Expectations

where;r* = assumed real rate of interestIP = Inflation PremiumRisk & Return: CAPM ModelCAPM Equation:

Changes in Risk AversionThe slope of SML reflects the degree of aversion. Risk premiums increase with increasing risk avoidance Therefore, changes in risk aversion shifts SML.

Changes preference of investors attributed by economic, political and social events:Stock market crashAssasination of political leaderOutbreak of war

Generally, expectations of hard times ahead tend to cause investors to become more risk averse require higher returns as compensation for accepting the risk.Risk & Return: CAPM ModelCAPM Comments:

CAPM generally relies on historical dataRequired returns can be viewed only as rought approximation since the beta may not reflect future variability of returns.CAPM is developed to explain the behavior of security pricesThis is based on assumed efficient market having same characteristics: Same information with respect to securitiesNo restrictions on investmentNo taxesRational investorsSimilarly risk averse

RISK and RETURNRisk and return are the two key determinants of the firms value. The financial manager can expect to achieve the firms goal of increasing its share price by taking only actions that earns returns at least commensurate with their risk.Therefore, Financial Managers need to recognize, measure and evaluate risk-return trade-offs to ensure that their decisions will contribute to the creation of value for owners.

Risk and Return - Presentation

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