Describe how DNA replication occurs.
Intro to Finance- Exam 2 Notes from 3/1 and 3/15 Value = Cash Flow / ( 1 + k )^t 1. Foundations of Risk Analysis a. Risk- A measure of relative variability of possible outcomes over time 2. Utility Theory and Risk Aversion a. Are people risk seekers or risk averters i. Risk Seekers: Las Vegas, Gamblers ii. Risk Averters: Buy Insurance, Diversify b. An experimental example i. Toss a fair coin: Heads You Win Tails You Lost i. $10 $9 ii. $100 $75 iii. $68,000 $32,000 ii. Utility Curve- Diminishing Marginal Utility for wealth each dollar gives you less satisfaction 1. KEY: The only thing that changed was the width of the distribution NOT the probability of winning or losing THEREFORE we don’t like wide distributions risk iii. Methods for describing the risk of an asset held in isolation 1. Standard Deviation- square root of variance a. Absolute measure of risk 2. Coefficient of variation- relative variance risk/return a. Expressed in absolute terms- used to evaluate the dispersion of outcomes b. SD / Expected Value iv. Measuring the Rate of Return 1. Arithmetic Average Return- a simple average return a. We invest $100, at the end of year 1, we have $150, a 50% return, and at the end of year 2 we have $75, a -50% return. The arithmetic average is (+50%, -50%)/2 = 0% 2. Geometric Average- the compound average return a. Use your financial calculator and solve for i 3. Risk and Return in a Portfolio a. Return in a Portfolio i. The expected return on a portfolio is simply the weighted average expected return on the individual securities in the portfolio 1. Simple Weighted Average ii. Risk in a Portfolio- return doesn’t diversify away 1. The expected SD of a portfolio is generally less than the weighted average SDs of the individual securities 2. Diversification reduces risk 3. Ex. Graphical Illustration a. Move to the Bahamas and sell umbrellas when it rains and sunglasses when it’s sunny 4. The riskiness of a portfolio is not the weighted average of the individual securities standard deviations a. When you combine things that don’t move perfectly with each other you can reduce risk 5. Mathematical formula for the SD of a portfolio a. Wa = weight or fraction of total funds in asset A b. Wb = “ “ “ “ B c. SDa = SD of asset A d. SDa = “ “ “ “ B e. Pab = correlation coefficient between assets A & B 6. The key in diversification is the correlation coefficient between the 2 assets 7. Example: Mathematical Illustration a. Assets SD Weights (w) SD * W A 20% 2/3 13.33 B 40% 1/3 13.33 Weighted average = 26.66% If Pab = 1.00 if Pab = 0.00 if Pab = -1.00 26,68% (= W.A.) 18,9% 0% 8. The Process of Random Diversification in a Portfolio iii. Risk in a Portfolio- Systematic and Unsystematic Risk 1. Unsystematic Risk (Diversifiable or Company Specific Risk) a. The part of the risk that can be eliminated through random diversification 2. Systematic Risk (Nondiversifiable or Market Risk) a. That part of risk that cannot be eliminated through random diversification 3. Risk associated with a $10 investment in one stock versus $1 in 10 randomly picked stocks 4. Sources of Risk Categorized Systematic Risk Unsystematic Risk - Intentional Risk - Management Risk - Recessions - Industry Risk - Terrorism iv. What Risk Should Be “Priced” 1. Why should investors expect a return on something that they can eliminate for free They shouldn’t 2. Only systematic risk contributes to the riskiness of a portfolio v. How Do We Measure Systematic Risk 1. Risk that cannot be diversified away is actually risk that affects all securities 2. To measure systematic risk we measure the tendency of a stock to more relative to the market a. S&P 500 3. We use characteristic lines showing the relationship between the security’s returns and the market’s returns to measure systematic risk 4. The slope of the characteristic line, called the beta is a measure of the stock’s systematic or market risk 5. The average beta for a stock is 1.00 a. B > 1, amplifies the market movement b. B < 1, mutes market movement 6. Since the beta of a portfolio is the weighted average of the individual securities betas, the security’s beta coefficient determines how that stock effects the riskiness of a diversified portfolio 7. EXAM – Calculate the beta of this portfolio- he’ll give us the weights a. Multiply = stock weights * betas, and then add them up vi. Require Rates of Return- Capital Asset Pricing Model 1. CAPM assumes: a. No bankruptcy costs b. People are rational 2. The security market line (SML) provides us with the theoretically correct required rates of return 3. MEMORIZE: Expected Rate of Return = Risk Free Rate + Beta (Return on market – risk free rate) vii. Measuring Systematic Risk for Individual Securities 1. Coefficient of determination, p^2, is the percent of variability explained in the regression 2. Implications: viii. The Assumption that Doesn’t Hold: Bankruptcy Costs are Zero 1. Systematic risk, in theory, is the only priced risk because it is the only risk you can’t eliminate for free 2. Do we care if the firm has unsystematic risk theory says no 3. But if unsystematic risk can cause bankruptcy and there are bankruptcy costs, then we don’t want systemic risk 4. Bankruptcy costs include: a. Lawyers b. Lost sales due to warranty concerns c. “Lemon Problem”- good employees leave and bad ones are stuck ix. Summary 1. The required rate of return equals the risk free rate plus a return to compensate for taking on added risk 2. The CAPM says that the beta is the appropriate measure of risk 3. Unfortunately measuring the beta for an individual security is very difficult 4. Bankruptcy costs also mean unsystematic risk is priced 5. Still the CAPM provides a framework for understanding risk Stock Re-Cap from 3/15: Oil prices drop and retails scales came up (from being way down) Measuring a Stock’s Risk Valuation of Financial and Real Risks 1. Valuation Principles a. Value = PV b. Net Value = PV – PV(costs) 2. Bonds- Valuation a. Bond Price = Present Value of Interest + Present Value of Return 3. Bond Valuation Principles a. There is an inverse relationship between interest rates and bond prices i. IR ^ then BR go down, vice versa b. The bond’s price will be below the par value ($1,000)- selling at a discount- if the investor’s required rate of return is aboce the bond’s coupon interest rate i. Bond Return = Return from interest payments +/- gain or lose from movement to par c. The longer the maturity the greater the fluctuation as interest rate changes d. The higher the coupon interest rate the less the bond fluctuates as interest rate changes e. At maturity the bond’s price equals its par value f. The calculated YTM isn’t necessarily the expected YTM i. But, there is default risl associated with corporate bonds ii. What we have calculated with the YTM is really the promised YTM iii. This calculated or promised YTM can be an optimistic estimate of the actual YTM the bondholder will earn g. What should you be investing in if you expect interest rates to increase i. Short maturities ii. High coupon interest rates In-Class Examples: What’s the value of a bond with 30 years to maturity, a coupon i-rate of 10% pays interest semi-annually, had a required rate of return of 8% (the YTM on similar bonds is 8%) par value N = 60 I = 8%/ 2 = 4% PV = = 1226.23 PMT = 50 FV = 1,000 What’s the value of a bond that pays 7% interest semiannually, for a maturity of 20 years, par value = $1,000, required rate of return (YTM) of 10% N = 20*2 = 40 I = 10/2 PV = = -742 PMT = 35 FV = 1000 What’s the yield to maturity (YTM) on a bond with 20 years to maturity, selling for $800, with coupon i-rate = 10% compounded semi- annually, and $1,000 par value N = 40 I = = 6.3962 * 2 = 12.8% PV = -800 PMT = 50 FV = 1,000