Investment Planning: Asset Pricing Models (Module 13)

What are the three conditions that define an arbitrage portfolio?

- Self Financing: Does not require additional funds from investor. - Riskless: There is no sensitivity to any factor; there is zero variance and covariance with other portfolios; and there is negligible nonfactor risk. - Positive Return: The riskless arbitrage will result in a positive return.

CML: What are the two key numbers that characterize the equilibrium in the securities market?

- The first is the vertical intercept of the CML, that is, the risk-free rate. It is often referred to as the reward for waiting. - The second is the slope of the CML, which is often referred to as the reward per unit of risk borne.

The Black-Scholes-Merton model has two limitations, what are they?

- cannot compute stocks that pay dividends - cannot compute American options and only European options

Which of the following statements concerning risk tolerance is (are) correct? 1. Emotions can severely limit a person's ability to make rational decisions about risk. 2. A person with a low net worth who has a $5 million umbrella liability policy is highly tolerant in financial matters.

1 A person who has a low net worth and a large umbrella liability insurance policy is probably risk averse.

Modern "asset allocation" is based upon the model developed by Harry Markowitz. Which of the following statements is/are correctly identified with this model? 1. The risk, return, and covariance of assets are important input variables in creating portfolios. 2. Negatively correlated assets are necessary to reduce the risk of portfolios. 3. In creating a portfolio, diversifying across asset types (e.g., stocks and bonds) is less effective than diversifying within an asset type. 4. The efficient frontier is relatively insensitive to the input variables.

1 Answer I is correct because the input variables like risk, return, and standard deviation (therefore covariance) are important to creating the frontier (the sensitivity of the frontier). Answer II is incorrect because anything less than +1.0 correlation coefficient reduces the standard deviation. Negatively correlated assets aren't necessary. Anything less than +1.0 will reduce risk. Answer III is incorrect. Diversifying across different stock and bonds types is more important than diversifying within an asset type (GM, Ford, Mercedes, BMW, etc.). Answer IV is incorrect because of Answer I. NOTE: This is a CFP Board released question that was previously used on the Certification Examination.

The capital market line is tangent to the efficient frontier. The risk-free asset is a Treasury bill. Which of the following statements about the CML are true? 1. The capital market line becomes the new efficient frontier. 2. As an investor moves from the point of tangency toward the risk-free rate, the percentage of long-term bonds in the portfolio increases. 3. The portfolio at the point of tangency includes an equal proportion of stocks and bonds. 4. As an investor moves from the point of tangency toward the risk-free rate, the percentage of Treasury bills in the portfolio increases.

1, 4 The risk-free rate reflects returns on T-bills. All points on the CML now dominate the original frontier and therefore become the new efficient frontier. At the point of tangency, the portfolio consists of a proportionate percentage of all possible risky assets, not just stocks and bonds.

What are the four factors?

1. Changes in the rate of inflation 2. Changes in the index of industrial production 3. Changes in the yield spread between high-grade and low-grade corporate bonds, a measure of investor confidence 4. Changes in the slope of the term structure of interest rates, as measured by the difference between the yields on long-term government bonds and T-bills

Emma is evaluating a stock. She notes that the market is generating a return of 8%. The risk-free rate is at 2.5%. The investment has a beta of 0.9. How much should the stock yield for a return?

2.5 + .9(8-2.5) = 7.45%

If Rm (the return on the market) is 10% and Rf (the risk-free rate) is 6%, then what is the stock risk premium if the security has a beta of 1.4? a. 5.6% b. 14% c. 10% d. 8.4%

A (10% - 6%) x 1.4 = (0.04) x 1.4 = 5.6%

Binomial option pricing is which kind of model? a. Valuation b. Volatility c. Pricing d. Variability

A Like Black-Scholes, it is a valuation model. Prices are established through the action of buyers and sellers; investors and analysts use valuation models to estimate what those prices should be.

Prospect theory

A behavioral finance model that is based on the concepts of "mental accounting" and loss aversion. Mental accounting describes investor propensity to segment their money into separate accounts. Loss aversion shows that investors are much more risk adverse when facing gains, and significantly less risk adverse when facing losses.

CAPM: Security Market Line (SML)

According to the CAPM, in equilibrium, the risk premium on any asset is equal to its beta times the risk premium on the market portfolio. This relation is called the SML. It is an equilibrium relationship between the expected return and covariance with the market portfolio for all securities and portfolios. The slope of the SML is the risk premium on the market portfolio.

Put-call parity: what happens if interest changes?

As the risk risk-free interest rate increases, the greater the discounting, which, in turn, decreases K or the strike price. So the increase in the interest rate will lower the strike price and increase the value of a call option but decrease a put option.

BAPM: Asset Segregation

Asset segregation is used to describe the behavior of individuals who look at an investment in isolation and do not consider the overall portfolio. This leads to mistakes because an investment in isolation may be more (less) desirable, but may be less (more) desirable when the entire portfolio is considered.

If the return on the market (Erm) is 12% and the risk free rate (rf) is 5%, what is the stock risk premium if the security has a Beta of 1.25? a. 5.75% b. 8.75% c. 6.28%

B (12% - 5%) x 1.25 = 8.75%

Which of the following is true about arbitrage pricing theory? a. The expected value of each factor is zero. b. Unexpected changes in inflation and unanticipated shifts in risk premium will influence security prices. c. Security movements are explained by a relationship between risk and return. d. Pricing of securities in different markets can differ for significant lengths of time.

B APT says unanticipated shifts in risk premium will influence security prices.

BAPM: Biased Expectations

Biased expectations are the term used to describe "overconfidence." Investors are overconfident in their prediction abilities, and therefore make mistakes concerning asset allocation, market selection, and market timing.

In the APT model, when a factor is zero, which of the following is true? a. The factors have an impact on the return. b. It's unexpected or unanticipated. c. It's expected or anticipated.

C When a factor is zero, the factor has no impact on the return because it is expected or anticipated.

Put-Call Parity (Formula)

C - P = S - PV (X) C = price of call P = price of put S = market price of underlying stock PV(X) = present value of the strike price = = X / (1+r)^T r = risk-free rate T = time to expiration date

Security X has a current put price of $3, a strike price of $20, a market price of $22, and 30 days till expiration. If the risk-free rate is 1.5%, what is the current price of a call for security X for the same strike price and maturity?

C - P = S - PV(X) C = S - PV(X) + P (Tip: Add P to each side to isolate C) C = S - [ X / (1+r) T ] + P (Tip: Present value of the strike price.) C = 22 - [20 / (1.015)(30/365)] + 3 C = 22 - [20 / 1.0012] + 3 C = 22 - [19.98] + 3 C = $5.02

Supply & Demand for Stock: CAPM vs. BAPM

CAPM: Determined by standard beta, which is utilitarian in nature. BAPM: Determined by the behavioral beta, which is both utilitarian and value-expressive.

Expected Returns: CAPM vs. BAPM

CAPM: Determined by standard betas, measures of systematic risk that are determined with respect to the market portfolio. BAPM: Determined by behavioral betas, measures of risk with respect to the mean-variance-efficient portfolio. This portfolio differs from the Markowitz market portfolio and depends on the preferences of the noise traders (e.g., whether growth or value stocks are currently favored).

Model Premise: CAPM vs. BAPM

CAPM: Presence of Markowitz-based information traders who have specific mean-variance preferences and do not commit cognitive errors. BAPM: Market interaction between information traders and noise traders, who do not have mean-variance preferences and do commit cognitive errors.

Beta: CAPM vs. BAPM

CAPM: Standard betas are difficult to determine because selecting an approximate proxy for the market portfolio is difficult. BAPM: Behavioral betas are difficult to determine because the preferences of the noise traders can change over time.

Put-call parity: what happens if dividend yield changes?

Consider the following expanded put-call parity equation: C - P = S - PV(X) - D As dividend yield increases, the value of the call option decreases and the put option increases. After the dividend is paid, the stock price will drop, which will again lower the call option value.

If the risk-free rate is 4%, the beta on Intel is 1.1, and the rate of return of the market portfolio is 12.0, what is the expected return on Intel? A. 12.8% B. 11.2% C. 12% D. 13.1%

Correct Answer: A. 12.8% Explanation: The expected rate of return = 4% + (12.0 - 4) (1.1) = 12.8%.

Which model is predicated on the assumption that stock prices can move to only two values over a short period of time? A. BOPM B. CAPM C. APT D. Black-Scholes-Merton

Correct Answer: A. BOPM Explanation: The binomial option pricing model assumes that stock prices will attain one of two possible known prices at the end of each of a finite number of periods. The Black-Scholes-Merton model is a continuous time model. The CAPM and APT are not option pricing models.

What does the process of arbitrage take advantage of? A. Differential pricing B. Abnormal returns C. Low stock price D. Volatility of stock

Correct Answer: A. Differential pricing Explanation: Investors who take advantage of differential pricing for the same physical asset or security engage in the arbitrage process. Abnormal returns, low stock price and volatility of stock do not figure in the arbitrage process.

Which of the following is an important assumption of put-call parity? A. Both options may have different exercise prices but the same expiration dates B. Both options have the same exercise prices and the same expiration dates C. Both options will produce the same payoff on the stock as well as a risky bond D. Both options will produce the same payoff on the stock as well as another risky asset

Correct Answer: B. Both options have the same exercise prices and the same expiration dates Explanation: The payoff from buying a put option on a stock and a share of the stock will be the same as buying a call option on the stock and a risk-free bond. This is under the assumption that both options have the same exercise price and expiration date. This is called put-call parity.

One limitation to the Black-Scholes-Merton model is that strictly speaking it is only applicable to options that do not: A. Have an expiration date B. Pay dividends over the life of the option C. Display implied volatility D. Have an intrinsic value

Correct Answer: B. Pay dividends over the life of the option Explanation: One limitation of the Black-Scholes-Merton model is that it can only be applied to options that will not pay dividends over the life of the option. The other limitation is that it is applicable only to European options and not to American options.

Which one of the following is not a key assumption underlying the CAPM? A. Investors prefer portfolios with lower standard deviations. B. Assets are infinitely divisible. C. Investors may borrow or lend at a single risk-free interest rate. D. Taxes and transaction costs reduce market liquidity.

Correct Answer: D. Taxes and transaction costs reduce market liquidity. Explanation: The assumption regarding taxes and transactions costs under CAPM is that they are irrelevant. It is not assumed that they reduce market liquidity. The CAPM also assumes that investors are risk averse and therefore prefer portfolios with lower standard deviations. Other assumptions are that assets are infinitely divisible and that investors may borrow or lend at a single risk-free rate.

The following statements describe either characteristics of the Capital Asset Pricing Model (CAPM) or the Behavior Asset Pricing Model (BAPM). Select the statements that pertain to the BAPM. 1. Betas are determined with respect to the preferences of noise traders. 2. Supply and demand for a stock is utilitarian. 3. Determining Beta is difficult because the preferences of noise traders change over time. 4. Expected returns are based on beta, which is determined by the market portfolio. 5. Beta is determined using both utilitarian and value-expressive measures.

Correct Answers: 1, 3, 5 Explanation: BAPM is based on the interaction between information traders and noise traders, while CAPM only considers information traders. CAPM uses utilitarian factors in determining supply and demand for a stock, while BAPM also considers value-expressive measures.

The Black-Scholes-Merton formula calculates the fair value of an option based on five factors. Which of the following are included among those factors? 1. Taxes and transaction costs 2. Time remaining before expiration 3. Risk-free rate of return 4. Stock volatility

Correct Answers: 2, 3, 4 Explanation: The Black-Scholes-Merton formula shows that the fair value of an option is determined by the following five factors: stock price, exercise price, risk-free rate, life of the option and the volatility of the common stock. It does not consider taxes and transaction costs as a factor in determining the fair value of an option.

Which of the following statements is/are true? 1. Both the standard finance view and the behavioral finance view assume the investor to be "rational." 2. Investors make mistakes under the standard finance models. 3. Behavioral finance recognizes the contributions of standard finance. 4. Behavioral finance considers how investors act and feel. 5. Mental accounting is a key concept of "prospect theory."

Correct Answers: 3, 4, 5 Explanation: Investors, assumed to be "rational" under the standard finance view, do not make mistakes using these standard finance models.

Which of the following is true about the arbitrage pricing theory? A. Investors will take advantage of arbitrage opportunities thus eliminating them B. Investors will not act on arbitrage opportunities. C. Arbitrage has fewer assumptions than the CAPM. D. Arbitrage opportunities are expensive and risky.

Correct Answers: A. and C. Explanation: The logic behind APT is that investors will observe and take advantage of arbitrage opportunities and eliminate them. When all arbitrage possibilities have been eliminated, the equilibrium expected return on a security will be a linear function of its sensitivities to the factors.

In the equilibrium world of the CAPM, a security that is not part of the market portfolio: Click all that apply. A. Is not owned by investors B. Has an equilibrium price of zero C. Is attractive to the very risk-averse investor D. Has a market value of zero

Correct Answers: A., B. and D. Explanation: The market portfolio is the risky portfolio held by all investors. Therefore, a security that is not part of the market portfolio is not attractive to the risk-averse investor. An important feature of the CAPM is that in equilibrium each security must have a nonzero proportion in the composition of the tangency portfolio. That is, no security can, in equilibrium, have a proportion in the portfolio that is zero. Hence, the market portfolio is a set of securities that can be freely owned by investors.

Some common characteristics of the relevant factors of APT models include: A. Inflation B. Term structure of interest rates C. Price of gold D. Corporate earnings and dividends

Correct Answers: A., B. and D. Explanation: The most commonly identified factors that affect expected returns are indicators of aggregate economic activity, inflation and interest rates. Researchers have not identified the price of gold as a factor.

Under Black/Scholes, which of the following variables will decrease the value of a call option? a. An increase in interest rates. b. An increase in the price of the stock. c. An increase in the volatility of the stock. d. An increase in the strike price. e. An increase in the time to expiration.

D An increase in the price of the stock, the time to expiration, the volatility of the stock and in interest rates will increase the value of a call option.

Which of the two aspects of the CAPM is used for an individual security? a. Both CML and SML b. Neither CML nor SML c. CML d. SML

D The CML specifies the relationship between risk and return on a portfolio.

BLACK-SCHOLES-MERTON MODEL: Delta

Delta measures the impact of a change in the underlying stock price on the value of a stock option. Delta is positive for a call option and negative for a put option. A $1 change to the stock price is approximately equivalent to change in option price by delta dollars.

When the stock market suffered a 40% loss in 2008 Bob only had a loss of 25% of his investment value. Bob decided not to invest new money during the market downturn. His budget was very tight and he saved $200,000. His money was in a money market paying .1%. He had been watching the market in 2009. The first 3 months were a disaster to his investments. If had listened to the TV analysts during that time what do you think he would have done? a. Buy put options b. Sell his existing investments c. Buy call options d. Buy new investments with the $200,000 in the money market e. Nothing

E Probably do nothing. He is petrified about all the negative reporting. He cannot make a decision. He should have bought 9 month calls in 2009. He would have probably doubled or tripled his money in 2009.

BLACK-SCHOLES-MERTON MODEL: ETA

Eta measures the percentage impact of a change in the stock price on the option value. Eta is positive for a call option and negative for a put option. A 1% change to the stock price is approximately equivalent to change in option price by eta%.

BLACK-SCHOLES-MERTON MODEL: Gamma

Gamma measures delta's sensitivity to a stock price change. A $1 change in the stock price causes the delta to change by approximately the amount of gamma.

Put-call parity: what happens if strike price changes?

If the strike price increases, then S -PV(X) decreases, as will the call option price. If the strike price decreases, the opposite happens, and the put option premium will decrease. Therefore, changes in strike price are inversely related to price changes of the call option premium, and are directly related to price changes of the put option premium.

Put-call parity: what happens if stock price increases?

Increase call premium & decrease put premium

Put-call parity: what happens if strike price decreased?

Increase call premium & decrease put premium

Loss Aversion

Investors are more risk adverse when faced with gains and less risk adverse when faced with losses.

Biased Expectations

Investors are overly confident in their ability.

Cognitive Errors

Investors make mistakes.

Mental Accounting

Investors segment their money into separate accounts.

Capital Market Line (CML)

It can be described as the most desirable asset allocation line. It denotes the set of most desirable risky portfolios that can be generated by borrowing and lending at the risk-free rate of interest. Assuming homogeneous expectations and perfect markets, the CML therefore represents the efficient set.

BLACK-SCHOLES-MERTON MODEL: Rho

Rho measures the option price sensitivity to a change in interest rate. A 1% change to the interest rate will cause the option price to change approximately by rho.

BAPM: Self-Control

Self-control is a flaw that behavioral investors also exhibit. This is simply being caught up in the actions of "the crowd." The high-tech bandwagon in the late nineties serves as a good example of this behavior.

Put-call parity: what happens if underlying stock price changes?

Stock Price As stock price increases, S - PV(X) also increases. As the stock price decreases, then S - PV(X) will also decrease. Therefore, an increase in stock price will increase the call option premium and decrease the put option value.

Put-call parity: what happens if time remaining to expiration changes?

The greater the length of time, the more likely the option will move further in-the-money. Therefore, the longer the period before expiration, the higher the premium for the option. This is true for both calls and puts.

CAPM: Market Portfolio

The market portfolio is a portfolio consisting of all securities in which the proportion invested in each security corresponds to its relative market value. The relative market value of a security is simply equal to the aggregate market value of the security divided by the sum of the aggregate market values of all securities. In theory, M consists not only of common stocks but also other kinds of investments such as bonds, preferred stocks and real estate. However, in practice, some people restrict M to just common stocks - a procedure that may give inappropriate results in some applications.

Put-call parity: what happens if volatility of stock changes?

The more a stock price fluctuates, the further it can go in-the-money. Therefore, the more volatile a stock is, the higher the premium for the option. This true for both calls and puts.

CAPM: Separation Theorem

The optimal investment decision to buy the market portfolio is separate and independent from the financing decision about whether to borrow or lend to finance the investment in the market portfolio. The optimal combination of risky assets for an investor can be determined without the knowledge of the investor's preferences toward risk and return.

BLACK-SCHOLES-MERTON MODEL: Theta

Theta measures the option price sensitivity to a change in time till expiration. A one-day change to time to expiration will cause the option price to change approximately by theta.

Capital Asset Pricing Model (CAPM)

a model that relates the required rate of return on a security to its systematic risk as measured by beta. CAPM assumes that all investors are identical and invest in the same way with the same information.

BLACK-SCHOLES-MERTON MODEL: Vega

Vega measures the impact of a change in the volatility of the stock on the stock option. Vega is positive for both a call option and a put option. A 1% change to the stock's standard deviation is approximately equivalent to change in option price by vega.

arbitrage pricing theory

a model of stock prices that allows for more sources of risk than just the stock market's excess return One primary APT assumption is that each investor, when given the opportunity to increase the return of his or her portfolio without increasing its risk, will proceed to do so. The mechanism for doing so involves the use of arbitrage portfolios. An arbitrage portfolio is defined by three conditions: - Self Financing: Does not require additional funds from investor. - Riskless: There is no sensitivity to any factor; there is zero variance and covariance with other portfolios; and there is negligible nonfactor risk. - Positive Return: The riskless arbitrage will result in a positive return.

The Put-call Parity

allows investors to determine the price of a call option given information about a put option of the same security, strike price and expiration date, and vice versa. It illustrates the two option premiums as inter-related.

The Binomial Option Pricing Model

can be used to determine the fair value of an option based on the assumption that the underlying asset will attain one of two possible known prices at the end of each of a finite number of periods, given its price at the start of each period.

At the bottom of the market in March 2009, your client bought 10 options on a stock at $5. The options are 9 month calls that will expire in January 2010. The stock market and option price jumps to 20 by September. The client is following the stock each day. All of a sudden the market continues on but the option drops to 18. If the client sells now, he/she will have a $13,000 STCG ($18,000 - $5,000) that is reportable in 2009. What will the client do? a. Exercise the options (buy the stock) in January b. Wait and sell the options in January c. Sell the options in September d. Nothing

d S/he probably will not make a decision now. But s/he cannot do nothing because the options will expire in January. S/he could exercise the options in January, but we do not know what the exercise price is. What if it is $200 per share? That would cost $200,000 to exercise.

Put-call parity: what happens if decrease in volatility?

decrease call premium & decrease put premium

Study flash cards

did you study?

Put-call parity: what happens if decrease in dividend yield?

increase call premium & decrease put premium

Put-call parity: what happens if increase in risk-free rate?

increase call premium & decrease put premium

Put-call parity: what happens if their was a longer time to expiration?

increase call premium & increase put premium

Behavioral Portfolio Theory

presents the idea that investors build portfolios as "pyramids of assets." Each layer in the pyramid (e.g., emergency funds, investment portfolio, qualified retirement funds, etc.) carries different attitudes toward risk. This is completely different than the Markowitz model (CAPM), which is based on consistent attitudes toward risk

Cheri is trying to determine the return for a security that has a zero factor of 4%, expected return from economic growth of 8%, with sensitivity to the growth of 0.8. If the error term is 0, what is the return of this security?

r = .04 + (.8)(.08) = 10.4%

The Black-Scholes-Merton Option Valuation Model

requires use of a computer program or a table of natural logarithms and a table of cumulative normal distribution probabilities. It shows that the fair value of an option is determined by six factors: current market price of the underlying stock, exercise price of the option, risk-free rate of return, life of the option, the stock's dividend yield, and the risk or volatility of the common stock. It assumes that the risk-free rate and common stock volatility are constant over the option's life. The limitations of Black-Scholes-Merton option valuation model are that it is applicable only to European options and options on stocks that will not pay any dividends over the life of the option.

Value of the Factor

such as the rate of growth in industrial production

Zero Factor

the expected return when all factors = zero

The Behavioral Asset Pricing Model (BAPM)

was developed by Shefrin and Statman, the model improves on CAPM and its associated variations. The main difference between CAPM and BAPM is the presence of "noise" traders, who do not have specific mean-variance preferences and do commit cognitive errors.