F520 Asset Valuation and Strategy

F520 Asset Valuation and Strategy Overview Risk and Return F520 – Portfolio Concepts

Overview of Market Participants and Financial Innovation • What Types of Risk does a Corporation or a Financial Intermediary Encounter? F520 – Portfolio Concepts

Overview (Cont.) • How can Financial Products or Intermediaries reduce these risks F520 – Portfolio Concepts

Risk and Return - Outline • How is the return on an asset affected by the risk of the asset? • How do we measure risk and return on an asset? • Unique Risk (diversifiable, unsystematic, residual, or specific) • Market Risk(undiversifiable, systematic, or covariance) • Constructing Portfolios -- How do we measure risk and return on a portfolio of assets? • Choosing Stocks -- Development of the Efficient Frontier and use of Indifference Curves F520 – Portfolio Concepts

Outline - Cont. • More on Systematic Risk • Beta • The Capital Asset Pricing Model (CAPM) • Security Market Line (SML) • Obtaining Estimates of Beta • Uses of Beta • Tests of the Capital Asset Pricing Line and Beta. • Arbitrage Pricing Theory (APT), an alternative to CAPM F520 – Portfolio Concepts

Measuring Risk - Single Period P1 = the market value at the end of the interval P0 = the market value at the beginning of the interval D = the cash distributions during the interval F520 – Portfolio Concepts

Measuring Return - Multiple PeriodsArithmetic • Assumes no reinvestment of cash flows at the end of each period F520 – Portfolio Concepts

Measuring Return - Multiple PeriodsGeometric • Also referred to as Time-Weighted Rate of Return • Assumes reinvestment of cash flows at the end of each period. F520 – Portfolio Concepts

Measuring Return - Multiple PeriodsInternal Rate of Return • Also referred to as Dollar-Weighted Rate of Return • Allows additions and withdrawals • When no further additions or withdrawals occur and all dividends are reinvested, the Geometric and the IRR will yield the same F520 – Portfolio Concepts

Comparing Return CalculationsWithout Dividend (Income) Cash Flows F520 – Portfolio Concepts

Comparing Return CalculationsWith Dividend (Income) Cash Flows F520 – Portfolio Concepts

Measuring Total RiskVariance of actual returns • Measures of the dispersion of returns • Standard Deviation (STD)Standard deviation measures dispersion in percents F520 – Portfolio Concepts

Historical Returns, Standard Deviations, and Frequency Distributions: 1926-2009 F520 – Portfolio Concepts

Example Frequency Distribution • Frequency distribution is a histogram of yearly returns

Goal: Select the lowest risk portfolio • 0% stock, 100% bond • 20% stock, 80% bond • 40% stock, 60% bond • 60% stock, 40% bond • 80% stock, 20% bond • 100% stock, 0% bond F520 – Portfolio Concepts

Constructing Portfolios • Investors seek to maximize the expected return from their investment given some level of risk, or • Investors seek to minimize the risk they are exposed to given some target expected return. F520 – Portfolio Concepts

Constructing PortfoliosPortfolio Return • Expected Return of a Portfolio equals the weighted average return on the portfolioRp = wa * Ra + wb * Rb wa = weight of asset a wb = weight of asset b Ra = Expected return of asset a Rb = Expected return of asset b • General Formula • Weights must add to 1w1 + w2 + ... + wn = 1 F520 – Portfolio Concepts

Constructing PortfoliosPortfolio Variance • Two Asset CaseVar(Rp) = Var(wa * Ra + wb * Rb ) • General Case • for h  g • since 12 = 21, each covariance term is included in this equation twice. • i is the variance of asset i • gh is the covariance between asset g and asset h where F520 – Portfolio Concepts

Portfolio VarianceUsing Correlation • Correlation is the covariance standardized by the standard deviation of the two variables. • p = 1, perfect positive correlation • p = -1, perfect negative correlation • p = 0, no correlation • Two Asset Case • General Case F520 – Portfolio Concepts

Input Data A B Return 12% 16% Std. Dev. 10% 20% Correlation 1.00 Efficient FrontierCorrelation = 1 F520 – Portfolio Concepts

Input Data A B Return 12% 16% Std. Dev. 10% 20% Correlation -1.00 Efficient FrontierCorrelation = -1 F520 – Portfolio Concepts

Input Data A B Return 12% 16% Std. Dev. 10% 20% Correlation 0.00 Efficient FrontierCorrelation = 0 F520 – Portfolio Concepts

Portfolio Diversification Average annualstandard deviation (%) 49.2 Diversifiable risk 23.9 19.2 Nondiversifiablerisk Number of stocksin portfolio 1 10 20 30 40 1000 F520 – Portfolio Concepts

Efficient Frontier Conclusions • The covariance of two assets is important in determining the variance of a portfolio • As long as assets are not perfectly correlated, combining them in a portfolio reduces risk • Systematic risk cannot be eliminated by diversification because it is the covariance risk. Also called non-diversifiable or market risk, since it is primarily from economy wide factors. • Unsystematic risk (also called diversifiable risk, unique risk, or firm specific risk) comes from circumstances unique to the firm. This is why in a well diversified portfolio, unique risk is unimportant. F520 – Portfolio Concepts

Covariance – the key to diversificationMathematical Example • Assume a Special Case: Cov(i,h) = 0 • As our portfolio gets large, the variances of the portfolio gets vary small if all the covariances are 0. • If all assets have weight Yn then x = 1 / n • If the largest variance is V • As n gets large, this goes to zero. • Therefore, our portfolio choices are dominated by concern over the covariance terms. In other words, well diversified investors need only price the risk associated with the covariance of assets. F520 – Portfolio Concepts

Covariance the key to diversification- Intuitive Example F520 – Portfolio Concepts

Conclusions on Covariance • QuestionWhat will the addition of this asset to my portfolio do to my level of risk? • Answer:Look at the covariance of the asset with my portfolio, rather than the variance. F520 – Portfolio Concepts

Choosing Stocks • Investors maximize their welfare by choosing the: • Set of securities (investments) that maximize return for a given level of risk. • Set of securities (investments) that minimize risk for a given level of return. F520 – Portfolio Concepts

Input Data A B Return 6.5% 12% Std. Dev. 7.1% 16% Correlation 0.00 Efficient FrontierCorrelation = 0 QU: How do Investors Choose a Portfolio on the Efficient Frontier? F520 – Portfolio Concepts

Use Indifference Curves – measures of investor risk aversion QU: How Does this Change when a Risk-free asset is offered? F520 – Portfolio Concepts

Investors can move to a higher indifference curve – greater utility. QU: Can you identify the important parts in the graph. F520 – Portfolio Concepts

Important points on the graph. AAL – Asset Allocation orCML – Capital Market Line Borrowing Lending Market Portfolio Risk-free rate QU: What is meant by two-fund separation? F520 – Portfolio Concepts

Measuring Risk and Return for the CML • The risk free asset has no variance and its return is known with certainty (proxy – T-bill) • Portfolio Return on CML • Portfolio Risk on CML Standard Deviation is a linear function of the STD of the market portfolio F520 – Portfolio Concepts

Conclusions from Efficient Frontier and CML • As long as there are only risky assets, it makes sense for investors to hold a portfolio on the efficient frontier. The existence of a risk-free asset changes this. The new efficient frontier (called the capital market line) will connect the risk free asset to some risky portfolio. • The market portfolio (Rm) should be chosen because any other security will lead to a lower return for a given level of risk (Tangent portfolio). • All investors will hold some combination of the risk-free asset and the market portfolio, since this will maximize their risk-return trade-off. (called two-fund separation) • The CML portfolio chosen by an investor depends upon their risk aversion F520 – Portfolio Concepts

The Capital Market Line (CML) is Rp = Rf + slope (Standard Deviation) • The CML is a linear relationship between the efficient portfolio’s standard deviation and its expected return. QU: Can we transform the CML to another measure of risk which only accounts for systematic risk? F520 – Portfolio Concepts

SML, Beta, and CAPM • The CML shows that all investors must hold a combination of the risk-free asset and the market portfolio to maximize their utility. Furthermore, it shows that their is a linear relationship between risk and return. Knowing that two points make a line, let’s form the SML by plotting these points. F520 – Portfolio Concepts

Security Market Line • Ri= Rf + (Rm - Rf) • Where (Rm - Rf) is the slope of the line • Beta measures the risk of a stock in regards to the market portfolio (similar to the average stock). F520 – Portfolio Concepts

Understanding Beta and Calculating Portfolio Betas • Beta measures the relative volatility of stock i with the market portfolio. • The beta of a portfolio is the market value weighted average of the betas in the portfolio. F520 – Portfolio Concepts

Example: Portfolio Beta Calculations Market PortfolioStock Value Weights Beta (1) (2) (3) (4) (3) x (4) Haskell Mfg. $ 6,000 50% 0.90 0.450 Cleaver, Inc. 4,000 33% 1.10 0.367 Rutherford Co. 2,000 17% 1.30 0.217 Portfolio $12,000 100% 1.034 F520 – Portfolio Concepts

Beta, Expected Return and the Choice of Projects (Stock) • The concept that all assets must lie on the SML can also be Shown through an arbitrage argument. Consider Assets A, B, C, and D below. What will happen to the prices and expected returns of these assets in a competitive market using diversification techniques to eliminate all unsystematic risk? QU: How do I set up a trade to take advantage of this “mis-pricing”? F520 – Portfolio Concepts

Hedge Fund Example • How should I invest in these securities to take advantage of my expectations in returns relative to the required return. (Think about a hedge fund.) CML = 5+B(6) F520 – Portfolio Concepts

Hedge Fund Example • Some may think of having a net investment of zero, but look at the returns with market movements. None of our securities moved closer to efficiency in the example below. They each just followed the market as their risk would suggest. • How can we reduce our market risk while still taking a position on our expectations? F520 – Portfolio Concepts

Hedge Fund Example • How can we reduce our market risk while still taking a position on our expectations? • Wb*Bb + Wc*Bc + Wd*Bd = 0 [no market risk] • Wb + Wc + Wd = 0 [no investment for arbitrage] • Having a portfolio beta of zero immunizes the portfolio from the market changes, and allows us to profit only from the unsystematic movements in prices, which is where one would find “mis-pricing”. • Remember this still has risk (betas could be incorrect, our estimates of over- and under-pricing could be incorrect). • Controlling for market movements, you expect prices of securities with expected returns that are higher relative to the required return to increase and lower expected returns to decrease. F520 – Portfolio Concepts

Hedge Fund Example • The prior example showed no profit, because we assume that the returns on the stock were exactly equal to their expected return based on the market return and their beta. What is the hedge fund correctly predicted over and undervalued stocks? • Stock B is undervalued (Exp Ret > Req Ret), so we purchased a long position. Based on a market return of 10%, we expected it to increase 8% (market * beta), but our hedge fund model prediction was correct, adding 2%, so we made a net 10%. • Stock C is overvalued (Exp Ret < Req Ret), so we took a short position. Based on a market return of 10%, we expected it to increase 14% (market * beta), but our hedge fund model prediction was correct, reducing it by 2% for a net increase of 12%. Since we were short, we lost 12%. • Stock D is overvalued (Exp Ret < Req Ret), so we took a short position. Based on a market return of 10%, we expected it to increase 6% (market * beta), but our hedge fund model prediction was correct, reducing it by 2% for a net increase of 4%. Since we were short, we lost 4%. • Our portfolio has 0 beta and made money. F520 – Portfolio Concepts

Hedge Fund Example • What is the market had decreased in value? • Stock B is undervalued (Exp Ret > Req Ret), so we purchased a long position. Based on a market return of -10%, we expected it to decrease 8% (market * beta), but our hedge fund model prediction was correct, adding 2%, so we made a lost 6%. • Stock C is overvalued (Exp Ret < Req Ret), so we took a short position. Based on a market return of -10%, we expected it to decrease 14% (market * beta), but our hedge fund model prediction was correct, reducing it by 2% for a net decrease of 16%. Since we were short, we made 16%. • Stock D is overvalued (Exp Ret < Req Ret), so we took a short position. Based on a market return of -10%, we expected it to decrease 6% (market * beta), but our hedge fund model prediction was correct, reducing it by 2% for a net decrease of 8%. Since we were short, we made 8%. • Our portfolio has 0 beta and made money. • As long as our hedge fund model to predict over and under-valued stocks is correct, we make money in either an up or a down market. F520 – Portfolio Concepts

Uses of Beta • Discount rates in capital budgeting • Discount rates for pricing assets (stocks) • Utilities often base rates on the rate of return investors demand. • Cost of capital calculations • QU: What does the SML tell about the risk that managers should be concerned with when choosing a real asset investment (specifically a capital budgeting decision)? F520 – Portfolio Concepts

Estimating Beta – Characteristic Line • Ri= Rf + (Rm - Rf) • rearranging termsRi= Rf + *Rm - *RfRi= (1- ) Rf + * Rm • Characteristic Line (also called market model)Ri= ά + * Rm + eit • Where = covariance (Ri, Rm) / Var (Rm) • Based on the market model, we can also break down an assets total risk into systematic and unsystematic components.Total Risk = 2i = 2i2m + 2ei F520 – Portfolio Concepts

Differences in Beta Calculations • Merrill Lynch – 5 years of monthly returns • Value Line – 5 years of weekly returns • Historic Beta – Calculated with only the raw return data • Adjusted Beta – Begins with a firms historic beta and makes an adjustment for the expected future movement towards one. (Beta has been found to gradually approach 1 over time) • Fundamental Beta – Adjusts historic betas for variables such as financial leverage, sale volatility, etc. F520 – Portfolio Concepts

Data For Beta Calculation – Lilly StockCalculations in yellow, WRETD = Value weighted return, F520 – Portfolio Concepts

Data For Beta Calculation – Lilly Stock F520 – Portfolio Concepts

F520 Asset Valuation and Strategy