Explore BrainMass

Explore BrainMass

    Arbitrage Pricing Theory (APT)

    In the capital asset pricing model (CAPM), we look at how the interrelationship between securities contributes to the risk and, as a result, the expected return of a security. Both the arbitrage pricing theory (APT) and the CAPM demonstrate this same positive, linear correlation between risk and return. However, unlike the CAPM, the APT looks at how individual factors contribute to a security's return. Some factors are unsystematic - they only affect a single stock. These are factors such as the success of a company's research and development. Other factors are systematic - these factors affect more than one stock at the same time. Systematic risk is often referred to as market risk, and includes things such as inflation and interest rates. Using the APT, we see that the interrelationship between securities is dependent on the extent that these securities are affected by the same systematic factors.

    We therefore break the return of a stock into two main parts: the expected part of the return and the unexpected part of the return. That is to say, if a stock's return was always the same as its expected return - there would be no risk.

    R = the actual return on the stock
    = the expected part fo the return
    U = unexpected risk
    m = systematic risk, or market risk
    ε = unsystematic risk

    In the real world, stock returns have risk, and the value of a stock in any given month often changes based on new information about the factors that affect the stock's future prospects and its risk. This new information is often given in the form of an announcement. Here we have to be careful, because not all information provided in an announcement is unexpected. For example, the Federal Reserve might announce an interest rate hike on T-Bills from 1.5% to 2.5%. Investors may have already expected an interest rate hike of 0.5%, and this information may have already been discounted, that is, used by investors in evaluated the expected part of the return of the stock. The portion of the information therefore that is a surprise, is a factor in the unexpected return - in this case, the 0.5% rise in interest rates investors did not expect.

    Like the CAPM, we use a beta coefficient to represent how the price of a stock moves relative to surprise factors that make up the systematic risk. In the following, FEI is the surprise factor, equal to the surprise change in expected inflation, and βEI relates how this change affects the actual return on the stock. The subscripts r and IP refer to unexpected change in interest rates and unexpected change in industry production respectively. As you can imagine, a factor model like the APT can be built with many different factors, and no one model is the right model.

    Using the APT, we can also build a model for the return for a portfolio. The return on a portfolio is equal to the weighted average of the returns on each individual stock, where X represents the proportion each stock is weighted in a portfolio. Here we want to use a one-factor model to simplify things. We can use a single factor in this case such as the return on a market index such as the S&P 500.

    As we can see, the return on a portfolio is related to three sets of parameters:

    1. The expected return on each individual security,
    2. The beta of each security multiplied by the factor F
    3. The unsystematic risk of each security, ε

    In fact, we can find the return of the portfolio as (1) the weighted average of the expected returns on each stock, plus (2) the weighted average of the beta coefficients multiplied by the factor F, plus (3) the weighted average of each stock's unsystematic risk. In fact, the larger a portfolio is, the more the unsystematic risks of each stock counteract one another - eventually, with a large enough portfolio, (3) will be equal to zero.

    Let's take a look back at the security market line we introduced under CAPM. Security P represents our large portfolio (in this case, the market portfolio), or a security with equal beta and return to it. An investor can either invest in our portfolio, or in a combination of some other security and a riskless asset. An investor looking for higher risk, and higher returns, may invest in security A or B, or may leverage her investment by borrowing at the risk-free rate and investing in P. A low risk investor may invest in P, or may invest in some combination of A or B and a risk-free asset. No matter her risk tolerance, she can find a combination that suits her. Now consider security C. No investor would invest in a security with that much risk and only so much return. This security is overpriced, and in a competetive market its price will fall until it matches the security market line.

    A stock that has a beta of zero in this example always returns the expected return in our one-factor model. Similarly, for our very large portfolio, the weighted average of the betas of our portfolio will be equal to one. We could have a portfolio at A or B if we wanted to take on more risk, but let's say we're the average investor, so we want to invest at P. In fact, the stocks at A or B will have some beta higher than one. We can use this beta to determine the expected return for these stocks or portfolios. We know this relationship exists, because these portfolios can be duplicated by borrowing at RF and buying P: if a stock is overpriced, we would prefer to duplicate its risk and get a higher return by using this strategy, and if a stock is underpriced, market demand will push its price back up. Therefore, we end up with a relationship that looks like this, where is the expected return of any security lying on our security market line.

    Does this look familiar? It should. The capital asset pricing model uses beta to measure a security's responsiveness to movements in the market portfolio; whereas the APT uses beta to measure a security's responsiveness to different factors. When we use a one-factor APT model, we end up with a very similar formula to the capital asset pricing model. In fact, if the factor we decide to use in our one-factor model is change in the market portfolio, the APT and the CAPM are identical.

    Photo by Markus Spiske on Unsplash

    © BrainMass Inc. brainmass.com August 15, 2022, 11:05 am ad1c9bdddf

    BrainMass Solutions Available for Instant Download

    Computing Net Profit for Customer

    Wizard Corporation has analyzed their customer and order handling data for the past year and has determined the following costs: Order processing cost per order $7 Additional costs if order must be expedited (rushed) $9.50 Customer technical support calls (per call) $12 Relationship management costs (per

    Calculating Treasury Bills' Current Price Based on Implied Yield

    The Bank of Bermuda recently issues $1.3 billion of 98-day treasury bills on behalf of the federal government. The average bid received for the auction implied a yield of 3.114 percent. a. How much money was raised for the federal government? b. The high bid received implied a yield of 2.919 percent. If this were the averag

    Pricing in Absence of an Arbitrage Opportunity

    Consider the following prices from a McDonalds Restaurant: Big mac sandwich $2.99 Large coke $1.39 Large Fry $1.09 A McDonalds Big Mac value meal consists of a Big Mac sandwich, large Coke, and a large fry. Assuming that there is a competitive market for McDonalds food items, a

    Insuring absence of an arbitrage opportunity

    Consider the following prices from a McDonalds Restaurant. Big mac sandwich $2.99 Large coke $1.39 Large Fry $1.09 A McDonald's Big Mac value meal consists of a Big Mac sandwich. Large Coke and a Large Fry. Assuming that there is a competitive market for McDonald's food items, at what p

    Recovering From Service Failure in the restaurant business

    Recovering from a service failure requires different strategies and techniques for a hotel serving business travellers than for a restaurant serving family dinners. State whether you agree or disagree. Also in your response, formulate and share an action plan for an effective service guarantee for one of these types of busine

    GNC: Dividend Growth, CAPM, APT

    GNC company. 1. Which of the three models (dividend growth, CAPM, or APT) is the best one for estimating the required rate of return or discount rate of GNC? And Why? 2. Based on analysis and findings, what would you recommend to the board of directors of GNC company? Please examine: -the ease of use of these three mod

    Arbitrage with Forward and Option Contracts

    Suppose that the Euro-USD spot and forward exchange rates are as follows: Spot 1.34 90-day forward 1.3380 180-day forward 1.3348 What opportunity is open to an arbitrageur when a 180-day European call option to buy 1 Euro for $1.3083 costs $0.02 per Euro? Assume the size of forward and options contracts to be 1,

    Corporate Finance Questions: Bonds, Treasury Bills, and ATP

    P7-11 Each of the following statements is dangerous or misleading. Explain why. a. A long-term United States government bond is always absolutely safe. b. All investors should prefer stocks to bonds because stocks offer higher long-run rates of return

    Importance of Good Talking in Communication

    1. Much of the oral communication that goes on in business is the informal, person-to-person communication that occurs whenever people get together. Analyze and explain how the elements of good talking help us to communicate better? 2. Understanding the differences between virtual and face-to-face presentations is certainly b

    Arbitrage Opportunity

    Suppose that the premium on a European put option, p = $3. The time to maturity, T = 1 year. The strike price is $20. The stock price of the underlying common stock is $12 today. The risk-free interest rate is 8% per annum. The stock does not pay dividends. Observe that there is an arbitrage opportunity. Clearly state what

    Performance Evaluation

    Compare and contrast the use of the trait rating theory versus the goal achievement theory, including when it would be preferable to use one method over another.

    Example Finance Questions

    1."The implication of Systems Theory, is that things do not only simply happen, but rather they evolve from multiple pressures and can entail multiple outcomes" (Bowditch 2008). The systems theory, also known as the sociotechnical systems, is made up of four different parts. The first part is task/technological subsystem. This s

    Portfolio Theory: Stock Returns, Required Return, Risk Premium

    1. The standards deviation of stock returns for stock A is 40%. The standard deviation of the market return is 20%. If the correlation between stocks A and the market is 0.70, what is Stock A's Beta 2. An analyst has molded the stock of Crisp Trucking using a two- factor APT model. The risk- free rate is 6%, the expected

    Economic theory of the third and first world countries

    Choose a third world country of your choice and using an economic theory of your choice, identify the parts of the economic environment of your chosen country and analyze its characteristics. Repeat the same for a first world country's economy of your choice.

    Cost equity estimates

    Estimate the cost of equity (expressed in percentages or in a decimal format) or the rate of return that Accuray's shareholders 'require'. Use the Capital Asset Pricing Model (CAPM) in order to estimate the rate of return that shareholders require on their investment. Show all calculations. How would you go about finding the

    Risk premium; no-arbitrage return;stock of over-under priced

    Consider the C. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1 and a beta of 0.8 on factor 2. Stock B has an expected return of 15%, a beta of 0.9 on factor 1 and a beta of 1.2 on factor 2. The risk premium on the factor 1 portfolio is 3%. The risk-free rate of return is 6%. a) What is the risk-premium

    Triangular arbitrage calculations

    I need to show how I calculated this problem. You are given these quotes by the bank: You can sell Canadian dollars (C$) to the bank for $.70. You can buy Canadian dollars from the bank for $.73. The bank is willing to buy dollars for 0.9 euros per dollar. The bank is willing to sell dollars for 0.94 euros per dol

    Covered Interest Arbitrage

    Assume the following information: Spot rate of Russian ruble = $.100 180 day forward rate of Russian ruble = $.098 180 day Russian interest rate = 6% 180 day U.S. interest rate = 5% Given this information, is covered interest arbitrage worthwhile for Russian investors

    Economics : key information

    As an international economist you have been asked to prepare a short speech which answers the following questions: Instructor Comments: The best papers are able to convey the core ideas of these theories in concise statements. For the discussion of the Ricardian model, and the Heckscher-Ohlin Model, first explain the

    Covered interest arbitrage in the USA

    Assume the current spot rate is C$1.2103 and the one year forward rate is C$1.1952. The nominal rish free rate in Canada is 3% while it is 4 % in the US. Using covered interest arbitrage you can earn an extra ____________profit over that which you would earn if you invested $1. in the US a. $0.003 b. $0.006 c. $0.008 d. $0

    MacGregor's complex Theory X and Theory Y

    Some theorists believe that people are basically trustworthy and that controls are unnecessary and counterproductive. Others believe that people are untrustworthy and we need to look over their shoulder. These are Douglas MacGregor's Theory X and Theory Y. What is your opinion on this complex issue?

    Arbitrage and Financial Decision Making

    6. Suppose the risk-free interest rate is 4%. a. Having $200 today is equivalent to having what amount in one year? b. Having $200 in one year is equivalent to having what amount today? c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?

    Arbitrage Opportunity (FIAT Stock)

    On the Milan boards, Fiat stock closed at EUR5.84 per share on Thursday, March 3, 2005. Fiat trades as an ADR on the NYSE. One underlying Fiat share equals one ADR. On March 3, the S/EUR spot exchange rate was $1.3112/EUR1.00. If Fiat ADR's were trading at $7 when the underlying shares were trading in Milan at EUR5.84, what coul

    Triangular Arbitrage Profit

    Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting ?0.7627/$1.00 and Credit Suisse is offering SF1.1806/$1.00. You learn that UBS is making a direct market between the Swiss franc and the euro, with a current ?/SF quote of 0.6395. Show how you

    One paragraph is required.

    As a manager of a large, broadly diversified portfolio of stocks and bonds you realized that changes in certain microeconomic variables may directly affect the performance of your portfolio. you are considering unsing and Arbitrage pricing theory (APT) approach to strategic portfolio planning and want to analyze the possible imp


    At time 0.5, the price of $1 par of a zero maturing at time 1 will be either $0.96 or $0.98. The current price of the zero maturing at time 1 is $0.94 and the current price of the zero maturing at time 0.5 is $0.97. Consider also a claim that pays off $1 at time 0.5 if the zero maturing at time 1 is worth $0.96, and 0 otherwis