Lecture 14 Empirical Survey and Application: CAPM
I. CAPM: testable implications A) Only non-diversifiable risk matters. - should not be able to "beat" the market using other information. B) Return is a linear function of covariance with the non-dive
Lecture 27 Index Derivatives continued.
I.
Index derivatives can be used to hedge risks for illiquid assets that seldom trade. Real Estate: real estate prices are highly correlated. While an individual house may seldom trade an index derived from t
Lecture 28 I. How to price a structured product. - Replicate the dynamic strategy used to compute the final settlement value. The current price often depends on future values of an underlying index or implied volatility.
Example: DGD
Merrill Lynch A
Lecture 25 Stock Index Derivative Markets
I. Stock Index options Stock Index options are options whose underlying instrument is a stock index. A) Cash Settlement Options on stock indexes are cash settled. Rather than taking delivery of an underlying
Lecture 24 Stock Options Continued
I. More Black-Scholes
A) Implied Volatility C = S*N(d1) Ee-rT N(d2) N(.) is the normal distribution d1 = {ln(S/E) + (r + .52 )T}/T1/2 d2 = d1 - T1/2 The one unknown in the Black-Scholes model is the volatility of
Lecture 23 Stock Options
Options Pricing continued A) Recall the binomial option model. Stock and Bond price t=0 B t =1 rB t=2 rrB uuS uS S dS ddS udS
Call price t=0 B t =1 rB t=2 rrB Max(uuS E , 0) Cu C Cd Max(ddS E, 0) Max(udS E, 0)
Recall the
Lecture 22
I.
A)
Option Valuation
Option pricing problem. Suppose I have a stock with price 50 and a risk- free bond with price 100. Next period the bond will be worth 105 (5% interest rate) The stock will be worth 70 if times are good and 30 if ti
Lecture 20 Futures: Empirical Survey
Papers refrenced in this lecture have been posted on the website in a folder called "futures research".
I Market Integration: - Futures and cash (spot) markets appear to be very integrated
No arbitrage opportuni
Chapter 6: The Primary Markets I. Overview A. Def. The primary market involves the distribution of newly-issued securities to investors. Why take a company public? The founders of a company are endowed with a risky cash flow that often comprises the
Chapter 7: Secondary Markets and Secondary Market Transactions Def. A secondary market in financial assets is one where existing securities are traded among investors. I. Overview A. Functions of Secondary Markets i. Price information ii. Liquidity i
Valuation of Debt Contracts and Their Price Volatility Characteristics
I Features of debt contracts. A) debt contracts are any contract which specifies a stream of fixed payments at prespecified times. In this class, we will focus on bonds, the most
Lecture 15 Empirical Survey and Application: APT
Suppose well diversified portfolios X, Y, and Z have expected returns described by the APT E[Rn ] = a + b1n f1 + b2n f2 + b3n f3 Where E[Rn ] is the expected return of n-th stock. Fk = the kth non-dive
Lecture 13 Risk & Return Theories II Cont. I. CAPM continued
The CAPM predicts that the expected return of security n will be a linear function of its "beta"
E[Rn ] = Rf + n fE[RM - RF ]g
Where the "beta" of security n is estimated via a linear re
Lecture 12 Risk & Return Theories II
I. The link between the Two Fund Theorem and "price of risk".
Recall the Two Fund Theorem from Risk and Return I. The investor's problem of choosing an optimal portfolio given Given N assets with respective expec
Lecture 11: Risk and Return I Continued
I. Risk and Return
A) We will de.ne the risk of any asset (or portfolio of assets) as its variance.
B) Expected Return of Portfolios Given N assets with respective expected returns r1 ; r2 ; :; rN , the expec
Lecture 10: Risk and Return Theories I
I: Why do some financial assets have historically higher returns than others? Over the past 10 years, Microsoft has enjoyed a higher return GM Differences like Microsoft/GM are not the result of picking winners
I. Stock Market Returns A)
Lecture 8 Perfect Markets and Efficient Markets A perfect market has competitively determined prices and no market frictions. A perfect market is a theoretical benchmark used for comparison. Competitively determined prices
Lecture 7 The Term Structure of Interest Rates Continued.
I. Overview A) Estimating implied forward rates from current rates B) Using implied forward rates to hedge future debt assets and obligations C) Trading strategies
II.
Estimating implied for
Lecture 5 Valuation of Debt Contracts and Their Price Volatility Characteristics Continued.
I.
Valuation continued. A) Recall the formula for modified duration:
MD =(P-1 )*[(1+y) -1 ]*{[a1 /(1+y)] + [2a2 /(1+y) 2 ] + [3a3 /(1+y) 3 ] +.+ [T(M+ aT )
Lecture 6 The Term Structure of Interest Rates
Math Note: The text is an excellent book, however, it has some shortcomings. In this chapter, the text transforms annual yields to semi-annual yields by dividing the annual yield by 2 rather than yannual
Lecture 18 Introduction to Financial Futures Markets
I. Futures Contracts
Definition: Futures Contract: An agreement that obligates a party to the agreement to buy or sell a fixed amount of a standardized commodity at a designated future date and a
Quiz VI Practice Problems Econ 435
1) X is the price of a call option with a strike of 90 on a stock currently trading at 100 with an implied volatility of 30% Y is the price of a call option with a strike of 90 on a stock currently trading at 110 wi
GSI: Rosanna Chan
Econ 435 Informal Guide to Exam II
Resources Lecture notes: Chapters: Practice Questions: 9-16 8-9 Exam II Practice Questions on Handouts in Ctools Lecture notes Quiz II and Quiz III CAPM handout given in section week of 10/16-10/2
Quiz V Practice Problems Econ 435 Fall 2001
1) The Risk-Free Rate is 5% A stock is currently worth $100. Each period the stock will increase or decrease by 25%. There exists a put option on this stock, with an $80 strike price. The put option expire
Chapter 15: Stock Options Market - option price from Black-Scholes formula is fair in that it ensures that riskless arbitrage cannot take place - model assumes that the variance of the stock price is constant over the life of the option and that it i