Course 3: Module 13 Asset Pricing Models
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? 5.75% 8.75% 6.28%
(12% - 5%) x 1.25 = 8.75%
Some common characteristics of the relevant factors of APT models include: (Select all that apply) 1. Inflation 2. Term structure of interest rates 3. Price of gold 4. Corporate earnings and dividends
1, 2, and 4 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.
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? 12.8% 11.2% 12% 13.1%
12.8% The expected rate of return = 4% + (12.0 - 4) (1.1) = 12.8%.
Under Black/Scholes, which of the following variables will decrease the value of a call option? An increase in the price of the stock. An increase in the time to expiration. An increase in the volatility of the stock. An increase in the strike price. An increase in interest rates.
An increase in the strike price. 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 model is predicated on the assumption that stock prices can move to only two values over a short period of time? BOPM CAPM APT Black-Scholes-Merton
BOPM 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.
Which of the following is an important assumption of put-call parity? Both options may have different exercise prices but the same expiration dates Both options have the same exercise prices and the same expiration dates Both options will produce the same payoff on the stock as well as a risky bond Both options will produce the same payoff on the stock as well as another risky asset
Both options have the same exercise prices and the same expiration dates 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.
Which of the following statements concerning risk tolerance is (are) correct? Emotions can severely limit a person's ability to make rational decisions about risk. A person with a low net worth who has a $5 million umbrella liability policy is highly tolerant in financial matters. Neither I, II II I
I A person who has a low net worth and a large umbrella liability insurance policy is probably risk averse.
Risk-free rate of return
In the CAPM world, the expected return of a security with a beta of zero equals this rate of return.
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.
Total risk of a security
It is composed of market risk and non-market risk.
In the APT model, when a factor is zero, which of the following is true? The factors have an impact on the return. It's unexpected or unanticipated. It's expected or anticipated.
It's expected or anticipated. When a factor is zero, the factor has no impact on the return because it is expected or anticipated.
Which of the two aspects of the CAPM is used for an individual security? Both CML and SML CML SML Neither CML nor SML
SML The CML specifies the relationship between risk and return on a portfolio.
What is the major difference in the SML AND CML formula?
SML= beta, just looking at the security CML=standard deviation, allows you to plot new efficient frontier
Standard Finance versus Behavioral Finance:
Standard finance and its associated models such as CAPM, APT, Black-Scholes-Merton, and EMH assumes investors to be "rational" and also assumes an equilibrium-based market. Behavioral finance states that investors are "normal" and make decisions based on the way they feel about situations. Behaviorists argue that investors are human and are prone to make mistakes, such as cognitive errors and poor decisions made with biased expectations.
Which one of the following is not a key assumption underlying the CAPM? Investors prefer portfolios with lower standard deviations. Assets are infinitely divisible. Investors may borrow or lend at a single risk-free interest rate. Taxes and transaction costs reduce market liquidity.
Taxes and transaction costs reduce market liquidity. 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.
APT vs SML
The APT requires fewer underlying assumptions and includes a wider array of variables into the analysis than the SML. The APT is a more general theory than the SML. The APT can be shown to be mathematically equivalent to the SML when the market portfolio is the only risk factor in both models. Other similarities show that the two theories do not contradict each other. Moreover, the two theories are similar because both delineate undiversifiable commonalties that form the basis for risk premiums in market prices and returns. Since APT has been in existence for fewer years than the SML, it has not been tested as extensively. However, the results from initial tests look favorable.
Capital Asset Pricing Model (CAPM)
The capital asset pricing model (CAPM) enters the realm of positive economics by presenting a descriptive model of how assets are priced. The major implication of the CAPM is that the expected return of an asset is related to the measure of market risk for that asset known as beta.
Two key numbers characterize 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.
Non-market risk
The portion of a security's total risk that is related to events specific to the security and not to the movements in the market portfolio.
Market risk
The portion of a security's total risk that is related to movements in the market portfolio and hence to the beta of the security.
T or F: People have been shown to be more loss adverse than risk adverse.
True
Which of the following is true about arbitrage pricing theory? The expected value of each factor is zero. Security movements are explained by a relationship between risk and return. Pricing of securities in different markets can differ for significant lengths of time. Unexpected changes in inflation and unanticipated shifts in risk premium will influence security prices.
Unexpected changes in inflation and unanticipated shifts in risk premium will influence security prices. APT says unanticipated shifts in risk premium will influence security prices.
Binomial option pricing is which kind of model? Valuation Variability Pricing Volatility
Valuation 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.
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.
A main component of prospect theory is
cognitive errors. Institutional investors tend to "window dress," which is defined as the act of loading up their portfolios with recent winners just before the quarterly reports are due. This is due to the pressure they face by their plan sponsors to meet the performance of their benchmark portfolios in the short run. Studies have shown however, that "good companies" are not necessarily good "stocks" for investment purposes. Recent winners may not be the best investment prospects. A contrarian or value-approach may have better long-term growth potential.
Prospect Theory
is a behavioral-based model that attempts to explain phenomena such as investor preference for cash dividends and preference for stocks of "good" companies. Prospect theory can also address other problems in finance such as why do investors hate to realize losses?
The arbitrage pricing theory
is an alternative theory that has gained acceptance in the financial community. Under this theory, a security's price is explained by multiple economic factors (known as a multi-factor model) rather than the single systematic risk factor.
If a question on the certification exam begins to talk about factors and sensitivity to factors
it is referring to the APT.
Though buying a company's common stock may be riskier than bonds or preferred stock
it nevertheless gives the investor a stake in the company's future - for better or worse.
The binomial pricing model and the Black-Scholes-Merton pricing model
provide formulas for determining the price of options, that is, their premiums. Binomial option pricing models are mathematically simple models that have been developed to deal with a broad class of valuation problems that include options, stocks, bonds and other risky financial claims. The Black-Scholes-Merton model was the first closed-form option-pricing model.
The capital asset pricing model (CAPM)
provides an intuitive way of thinking about the return that an investor should require from an investment, given the asset's systematic risk. It suggests that investors need not worry about the market portfolio. They only need to decide how much systematic risk they wish to accept. Market forces will ensure that any stock can be expected to yield the appropriate return.
The capital market line (CML)
represents the linear efficient set in the world of CAPM. All investors will hold a portfolio lying on the CML. It is the efficient frontier when borrowing and lending at the risk-free rate are permitted. 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. The distinguishing feature of the capital market line is that the denominator is the standard deviation of the market. This will help you recognize the capital market line equation on the CFP® exam.
An economic equilibrium occurs whenever
supply equals demand. As a result, prices have no tendency to change.
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.
The Behavioral Asset Pricing Model
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.
The behavioral pricing model (BAPM)
was developed to improve upon CAPM. At the heart of the model is the study of behavioral finance, which acknowledges the contributions of standard finance, but argues that people are "normal" instead of "rational."
The intercept point of CML and efficient frontier
would result in the most efficient portfolio, called the tangency portfolio.
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? 10% 5.6% 8.4% 14%
(10% - 6%) x 1.4 = (0.04) x 1.4 = 5.6%
Identify the variables that represent the 'market risk premium' within the CAPM formula. ri = rf + (rm - rf)ßi rf + (rm - rf) (rm - rf)Bi (rm - rf) rf
(rm - rf) The 'market risk premium' is the difference between the market return and the risk-free rate [i.e., (rm - rf)]. This is the premium given to investors for taking on systematic risk. When multiplied by ß, it becomes the 'stock risk premium.'
Cheri is trying to determine the return for a security that has 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? 8% 12% 13.6% 10.4%
10.4% The one factor model for this security is r=.04+(.8)(.08)=10.4%
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.
Modern "asset allocation" is based upon the model developed by Harry Markowitz. Which of the following statements is/are correctly identified with this model? The risk, return, and covariance of assets are important input variables in creating portfolios. Negatively correlated assets are necessary to reduce the risk of portfolios. In creating a portfolio, diversifying across asset types (e.g., stocks and bonds) is less effective than diversifying within an asset type. The efficient frontier is relatively insensitive to the input variables. I and II only II and IV only I, II and IV only I only I, II and III only
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.
Which of the following is true about the arbitrage pricing theory? (Select all that apply) Investors will take advantage of arbitrage opportunities thus eliminating them. Investors will not act on arbitrage opportunities. Arbitrage has fewer assumptions than the CAPM. Arbitrage opportunities are expensive and risky.
Arbitrage has fewer assumptions than the CAPM. Investors will take advantage of arbitrage opportunities thus eliminating them. 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.
Which of the following statements is/are true? (Select all that apply) Both the standard finance view and the behavioral finance view assume the investor to be "rational." Investors make mistakes under the standard finance models. Behavioral finance recognizes the contributions of standard finance. Behavioral finance considers how investors act and feel. Mental accounting is a key concept of "prospect theory.
Behavioral finance recognizes the contributions of standard finance. Behavioral finance considers how investors act and feel. Mental accounting is a key concept of "prospect theory.
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. (Select all that apply) Betas are determined with respect to the preferences of noise traders. Supply and demand for a stock is utilitarian. Determining Beta is difficult because the preferences of noise traders change over time. Expected returns are based on beta, which is determined by the market portfolio. Beta is determined using both utilitarian and value-expressive measures.
Betas are determined with respect to the preferences of noise traders. Determining Beta is difficult because the preferences of noise traders change over time. Beta is determined using both utilitarian and value-expressive measures. 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.
Black-Scholes-Merton Model
Consider what would happen with the BOPM if the number of periods before the expiration date were allowed to increase. For example, if an option for company Z expires one year in the future, there could be a price tree with periods for each one of the approximately 250 trading days in a year. Hence there would be 251 possible year-end prices for the stock. The fair value of any call associated with such a tree would require a computer to perform calculations. If the number of periods were even larger, with each one representing a specific hour of each trading day, then there would be about 1,750 (= 7 x 250) hourly periods and 1,751 possible year-end prices. Note that the number of periods in a year gets larger as the length of each period gets shorter, and there will be an infinite number of infinitely small periods. Consequently, there will also be an infinite number of possible year-end prices. In this situation the BOPM given in the equation reduces to the Black-Scholes-Merton model, so named in honor of its originators. In a world not bothered by taxes and transaction costs, the fair value of a call option can be estimated by using the valuation formula developed by Black and Scholes. It has been widely used by those who deal with options to search for situations in which the market price of an option differs substantially from its fair value. A call option that is found to be selling for substantially less than its Black-Scholes-Merton value is a candidate for purchase, whereas one that is found to be selling for substantially more is a candidate for writing.
What does the process of arbitrage take advantage of? Differential pricing Abnormal returns Low stock price Volatility of stock
Differential pricing 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.
What does the process of arbitrage take advantage of? Differential pricing Abnormal returns Low stock price Volatility of stock
Differential pricing 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.
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? The capital market line becomes the new efficient frontier. As an investor moves from the point of tangency toward the risk-free rate, the percentage of long-term bonds in the portfolio increases. The portfolio at the point of tangency includes an equal proportion of stocks and bonds. As an investor moves from the point of tangency toward the risk-free rate, the percentage of Treasury bills in the portfolio increases. II, III I, IV I, III III, IV
I. The capital market line becomes the new efficient frontier. IV. As an investor moves from the point of tangency toward the risk-free rate, the percentage of Treasury bills in the portfolio increases. 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.
Which of the following points above and below the SML line are undervalued? I. A II. B III. C IV. D V. E I, II IV, V III
IV, V The expected returns are more than the required rate of return (SML).
Mental Accounting
Investors segment their money into separate accounts.
In the equilibrium world of the CAPM, a security that is not part of the market portfolio: (Select all that apply) Is not owned by investors Has an equilibrium price of zero Is attractive to the very risk-averse investor Has a market value of zero
Is not owned by investors Has an equilibrium price of zero Has a market value of zero 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.
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? Buy put options Nothing Buy new investments with the $200,000 in the money market Sell his existing investments Buy call options
Nothing 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.
Option Pricing Models
Option pricing models use formulas that permit an investor to compute put and call prices, or premiums, from certain variables. These option pricing models can be applied to options on stocks, options on stock market indexes, options on foreign currencies, and options on other underlying assets. A binomial option pricing model for valuing calls is presented first, followed by the Black-Scholes-Merton call-pricing model and the put-call parity formula. The put-call parity formula is used to determine put prices after call prices have been computed and to determine if the prices of puts and calls are aligned properly. If the underlying asset makes a cash payment, there is a formula to adjust the option price for that cash flow.
One limitation to the Black-Scholes-Merton model is that strictly speaking it is only applicable to options that do not: Have an expiration date Pay dividends over the life of the option Display implied volatility Have an intrinsic value
Pay dividends over the life of the optionYou correctly checked this. 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.
Given the following SML graph, on a risk-adjusted basis which of the following is true? Point B is more risky than Point A. The SML line represents the client's expected return. Point B is less risky than Point C. Point C is less risky than Point A.
Point B is less risky than point C based on risk-adjusted return. Risk-adjusted return is the return divided by beta. Point B is above the client's required rate of return line; therefore, it provides a better risk-adjusted return than point A. The SML represents the client's required rate of return. Of course, the client assumes more risk with Point B but not on a risk-adjusted basis.
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.
Limitations
The Black-Scholes-Merton model might seem to have limited use due to some drawbacks: - Almost all options in the United States are American options that can be exercised at any time up to their expiration date, whereas the Black-Scholes-Merton model applies only to European options. - The model is applicable only to options on stocks that will not pay any dividends over the life of the option. However, most of the common stocks on which options are written do in fact pay dividends.
Arbitrage Pricing Theory (APT)
The capital asset pricing model is an equilibrium model that describes why different securities have different expected returns. In particular, this economic model of asset pricing asserts that securities have different expected returns because they have different betas. However, there exists an alternative model of asset pricing that was developed by Stephen Ross. It is known as arbitrage pricing theory, and in some ways it is less complicated than the CAPM.
CML Calculation Example:
The market portfolio associated with a risk-free rate of 4% consisted of Able, Baker, and Charlie in the proportions of 0.12, 0.19, and 0.69, respectively. This is under the assumption that these stocks are the only ones that exist. The expected returns for the portfolio and standard deviation for the market portfolio with these proportions are 22.4% and 15.2%, respectively. The equation for the resulting CML is: r¯p=4+[22.4−415.2]σp=4+1.21σp
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? (Select all that apply) Taxes and transaction costs Time remaining before expiration Risk-free rate of return Stock volatility
Time remaining before expiration Risk-free rate of return Stock volatility 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.
What are the two main concepts of prospect theory?
are "mental accounting" and "loss aversion." The term mental accounting suggests that investors tend to segment their money in separate accounts. For instance, an investment may be made up of a "capital gain" account and a "dividend" account. If a stock price falls, then a loss has taken place in the capital gains account, while a dividend cut causes a loss in the dividends account. A behaviorist will frame the capital gains/dividend decision differently than will a standard finance, rational investor. The rational investor would view the investment decision as being consistent with the Miller-Modigliani dividend irrelevance theorem. That theorem suggests that in a world without taxes and transactions costs, an investor would be indifferent between capital gains and dividends. By selling appreciated securities, an investor could simply create "homemade" dividends. The standard finance view (Miller & Modigliani) does not address the fact that many investors prefer dividend-paying stocks, unlike the behavioral finance view (mental accounting). Loss aversion describes why many investors have been shown to be less risk adverse when faced with potential losses, and more risk adverse when faced with potential gains.
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.
The capital market line is
the linear efficient set of the CAPM. The CML represents the equilibrium relationship between the expected return and standard deviation of efficient portfolios. The separation theorem states that an investor's optimal risky portfolio can be determined without reference to the investor's risk-return preferences. The market portfolio is the risky portfolio held by all investors consisting of all securities, each weighted in proportion to its market value relative to the market value of all securities.
The Black-Scholes-Merton model
was the first closed-form option-pricing model.
