1 Finance School of Management FINANCE Review of Questions and Problems Part V: Chapter 13-15

2 Finance School of Management  In part IV （ Chapter ）, we have learned three most basic method of transferring risk: hedging, insuring, and diversifying.  In this part, we should further deal with the theory and practice of asset pricing: CAPM, Forward/Future, Option/Contingent Claim.

3 Finance School of Management Chapter 13: The Capital Asset Pricing Model （ CAPM ）  Main Contents: Theory--- to understand the:  CML-the relationship between CAPM and the Portfolio Selection Theory in chapter 12 Practice---to explain how to:  establish benchmarks for measuring the performance  SML-risk premiums on individual securities of investment portfolios （ active and passive portfolio management ）  infer the risk-adjusted discount rate to use in DCF models

4 Finance School of Management The Capital Market Line (CML) M rfrf Standard Deviation  Expected Return (%) CML Lending Borrowing E(r M )- r f MM In Equilibrium: aggregate demand should be equal to supply, which means tangent portfolio will become the market portfolio. Portfolio Selection Theory: all the investors will allocate their investments between the riskless asset and the same tangent portfolio.

5 Finance School of Management Implications of CAPM  Most investors would do just as well to passively combine the risk-free asset with an index funding holding risky asset in the same proportions as in the market portfolios as they would by actively researching securities and trying to beat the market.  CAPM is the risk premium on any individual security is proportional only to its contribution to the risk to the risk of the market portfolio. All the risk-reward combinations can be achieved simply by mixing the market portfolio and the risk-free asset, the only risk an investor need bear to achieve an efficient portfolio is market risk.

6 Finance School of Management From CML to SML CML In equilibrium, any efficient portfolio should be a combination of the market portfolio and the riskless asset. SML The best risk-reward depends on how much the market- related risk a portfolio bears.

7 Finance School of Management Applications of CAPM  Active and passive portfolio management---use CAPM to establish the benchmarks for measuring the performance of active investment  The risk-adjusted discount rate---use CAPM to infer the market-capitalized interest rate

8 Finance School of Management  Solutions: 13.2 – to use following three formulas correctly  To achieve a targeted return--the trade-off between expected return and risk (in equilibrium, the tangent portfolio is market portfolio)  CML  SML

9 Finance School of Management 13.3 –to derive the CAPM, we need:  market is in equilibrium—tangency portfolio is market portfolio  investors will select the same tangency portfolio homogeneous of information processing—investors agree on the distribution of returns homogeneous in behaviors—investors are behaving as mean-variance optimizers Portfolio SelectionCMLSML market-related risk is measured by the marginal contribution of individual security’s return to the standard derivation of market portfolio’s return Aggregate efficient portfolio should be formed by mixing the market portfolio and the riskless asset and CML is the risk-reward trade-off line in equilibrium Clear market

10 Finance School of Management –use CAPM to infer the price of stock  Step 1: to calculate the expected return of IBM *( ) = 25%  Step 2: pricing the IBM stock today (100 - x)/x = 0.25, then x = $80  Step 3: give the price of Exxon today $80 - $30 = $50 Application of the Law of One Price: if the price of a share of IBM today won’t be equal to the sum of the price of a share of GM stock plus the price of a share of Exxon, there will be opportunity to arbitrage

11 Finance School of Management –it needs to be examined that whether or not CAPM is a valid theory  In real world, we can see the return of individual security lies above or below the SML (equivalently, we say that it is under-priced or over-priced) the market isn’t in equilibrium or assumptions of homogenesis aren’t satisfied  CML provides benchmark for measuring the performance of investor’s entire portfolio of asset. however, SML provides different benchmark for performance of investor’s different partial portfolio Passive strategy serves as a benchmark, that it to say, CAPM implies that investor will do as well by simply combining market portfolio and the riskless asset Some index fund is used as a proxy for market portfolio

12 Finance School of Management Chapter 14: Forward and Futures Prices  Main Contents: Mechanism of future trading: margin requirement and daily marking to market (daily realization of gains and losses) Forward-spot price parity for commodities, currencies and securities How to use information inferred from the relations among spot and forward prices to generate arbitrage profits  Problems of homework: to give the right strategies for arbitrage when the price parity formulas are unsatisfied Law of One Price

13 Finance School of Management  Solutions: 14.1 – foreign-exchange parity relation  a. you should give the ways to hedge the exchange-rate risk  b., where F and S are the forward and spot price of the pound  c. borrowing dollars, investing in pounds and selling them forward at the inflated forward price Exchange 1 pound into S dollars in spot market and invest S dollars in the dollar-interest rate S*(1+r dollar ) Invest 1 pound in pound-interest rate and exchange it into dollars in the future (1+r pound )*F Cost = 1 pound

14 Finance School of Management 14.2 –forward-spot parity of bond  a. give the price of coupon bond- DCF approach  b. F=S(1+r)-D = *(1+3.5%)-4%*1000=  c. if the forward price is lower than the , then you should buy the bond at a lower forward price on the future market, so the strategy for arbitrage is: sell short a bond at $1, ; buy it forward at a lower forward price

15 Finance School of Management 14.7 –forward-price parity of commodity  a. implied riskless interest rate F=(1+r+s)*S, r =10%  b. if the riskless interest rate is less than 10%, the spot price of kryptonite is too low or the forward price is too high, so the strategy for arbitrage is: borrow at a lower rate, invest in hedged kryptonite, and simultaneously sell it forward

16 Finance School of Management 14.8 –implied carrying cost  implied carrying cost = forward price-spot price = riskless interest rate + storing cost which is the opportunity cost of buying the commodity in spot price which should be compounded

17 Finance School of Management Chapter 15: Options and Contingent Claims  Main Contents: – The principle of options – The characters of options (Volatility and Maturity) – The pricing of options Two-State Option Pricing: Binomial model Continuous-State Option Pricing: B-S model – Application of options pricing (CCA analysis) Corporate Debt and Equity Credit Guarantees Real Options

18 Finance School of Management  Solutions: 15.4 –the implications of put-call parity relation  a. replicate: E/(1+r)^T represents the price of a synthetic pure discount bond with face value of E and maturity of T to buy a share of stock, and a European put with exercise price $100, and sell a European call with an exercise price $100 a “unit” portfolio, which consists of long positions in one put and one share and writing one call

19 Finance School of Management  b. the rikless interest rate can be calculated directly from the parity formula  c. if the riskless interest rate is lower than rate in part b, the synthetic bond is sold at a lower price or the pure discount bond is over-priced, so you should borrow money (or sell short the pure discount bond) and buy a synthetic bond, that is to say, borrow at a lower interest rate, buy a share of stock, go on a long position in a European put with exercise price $100, and a short position in a European call with an exercise price $100

20 Finance School of Management 15.7 – the implications of put-call parity relation  a. From the put-call parity formula, P+S=E/(1+r)+C,we have r =0.084  b. if the riskless interest rate is higher than rate in part a, the synthetic bond is sold at a higher price or the pure discount bond is under-priced, so you should sell short a synthetic bond and loan money, that is to say, sell short a share of stock, go on a short position in a European put with exercise price $200, a long position in a European call with an exercise price $100, and buy a T-bill with coupon rate 9% invest in T-bills a “unit” portfolio, which consists of long positions in one put and one share and writing one call

21 Finance School of Management 15.9 – two-state option-pricing  create a synthetic call--borrowing y/(1+r) and buying x shares stock, then the cash flow at maturity is 150*x-y=65 50*x-y=0  by the law of one price, the call and its replicating portfolio (synthetic call) must have the same price, so the price of call option is 100*x-y/(1+r)

22 Finance School of Management 15.10–Black-Scholes option-pricing  to complete the calculations by Excel borrow buy shares continuous compounding

23 Finance School of Management 15.12–valuation of corporate securities with the binomial model  a & b. equity—as a call (underlying asset is firm’s asset, the exercise price is the face value of its outstanding debt, and the exercise date is the maturity date of its debt), that is to say, the firm’s shareholders hold a call option on the firm’s assets, which they can exercise by repaying the face value of the debt

24 Finance School of Management  c. debt—because of limited liability, the total payoffs to creditors are bonds =Min (value of the firm's assets, face value of the outstanding debt)  d. step 1: value of riskless bonds=E/(1+r) step 2: from the put-call parity formula, we have E/(1+r)=(S-C)+P, where S-C is the value of bonds issued by corporate because Asset (S) = Equity (C) + Liability step 3: the difference in value between the firm’s bonds and the corresponding default-free bonds equals the value of a European put on the firm’s assets (as collateral )