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ADMS 4501 Midterm > Lecture 4 - APT and Multifactor Models > Flashcards

Lecture 4 - APT and Multifactor Models Flashcards

1
Q

Arbitrage

A

When an investor can earn riskless profits without a net investment

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2
Q

Law of One Price

A

If 2 assets are equivalent in all economic aspects, they should have the same market price

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3
Q

Draw the efficient frontier

A

See slide 6

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4
Q

Purpose of the efficient frontier?

A

Helps you find the optimal mix of investments that give you the highest return for a certain level of risk

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5
Q

Optimal Portfolios

A

Portfolios on the efficient frontier that give you the best returns for your risk tolerance

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6
Q

Suboptimal Portfolios

A

Portfolios below the frontier and less efficient because they have more risk or less returns

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7
Q

Pricing Models

A
  • CAPM
  • APT
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8
Q

Which model is single factor?

A

CAPM

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9
Q

Which model is multifactor?

A

APT

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10
Q

Dominance Argument

A

Investors prefer:

Higher return with the same risk (variance), or
Lower risk with the same return (expected return).

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11
Q

Where do returns on securities come from?

A

1) Macro factors
2) Micro factors

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12
Q

E(Ri)

A

Expected return on an asset given its beta

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13
Q

F

A

Unanticipated change in macro-economic factor

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14
Q

ei

A

Firm specific events (non-systematic components)

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15
Q

Single Factor (CAPM) Formula

A

E(Ri) = Rf+ βi(Rm - Rf)

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16
Q

Market Risk Premium

A

Rm - Rf, where Rf is the t-bill rate of return

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17
Q

Total Risk can be separated into

A

1) Unsystematic Risk
2) Systematic Risk

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18
Q

Unsystematic Risk (Diversifiable)

A

Uncertainity inherent in a company or industry environment

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19
Q

Systematic Risk

A

Risk that affects the entire market, not just a stock or an industry

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20
Q

Draw a graph that illustrates systematic and unsystematic risk

A

See slide 16

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21
Q

Draw a graph that illustrates CAPM

A

See slide 19

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22
Q

Problems with CAPM

A
  • Beta is not stable
  • Difficulties in selecting a proxy for market portfolio
  • Many unrealistic assumptions
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23
Q

The expected return based on CAPM for a stock is 10.5%. If the risk-free rate is 4%, and market return is 9%, what is the Beta of this stock?

A

Expected CAPM Return = Rf + beta x (Rm - Rf)
0.105 = .04 + Beta (.09 - .04)
0.105 - .04 = .05Beta
0.065 = .05Beta
Beta = .065/.05 = 1.30

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24
Q

If you draw a regression line between the returns to the security over time and the returns to the market portfolio, the slope of this regression line is the:

A

Security’s beta

25
Q

F0

A

Risk-free rate

26
Q

F1

A

Factor 1

27
Q

F2

A

Factor 2

28
Q

Bi

A

Factor Beta

29
Q

ei

A

Firm specific events

30
Q

Multifactor (APT) Model

A

Ri = E(Ri) = F0 + βi1 F1 + βi2 F2 + ei

31
Q

Examples of factors

A
  • Market Risk Premium
  • GDP Growth rate
  • Expected inflation
  • Changes in interest rates
32
Q

APT

A

Arbitrage Pricing Theory

33
Q

Arbitrage Pricing Theory

A

Predicts an asset’s returns using a linear relationship between the expected return and several macroeconomic factors that capture systematic risk

34
Q

APT Assumptions

A

1) Capital markets are perfectly competitive.
2) Investors always prefer more wealth to less wealth.
3) Asset returns are determined by a linear relationship with several factors or indexes

35
Q

Consider the multifactor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1, and a beta of.8 on factor 2. The risk premium on the factor-1 portfolio is 3%. The risk-free rate of return is 6%. What is the risk-premium on factor 2 (i.e. the factor loading) if no arbitrage opportunities exist?

A

E(RA) = R f + β1 F1 + β2F2

16.4% = 6% + 1.4 (3%) + 0.8 x F2
10.4% = 4.2% + 0.8 F2
0.80 F2 = 10.4% - 4.2%
F2 = 6.2%/0.80 = 7.75%

Note, Rf and F0 are the same in this case

36
Q

What is the name of the model that is used in the real word and why?

A

Fama-French 3 Factor Model

Because APT doesn’t tell you where you should look for factors

37
Q

Consider Bank of America Corp. (symbol: BAC) that has a beta of 1.34 and a standard deviation of 25%. The return on the risk-free rate (T-bill) is 4.60% and the expected return on the S&P 500 index is 11% and its standard deviation is 22%. The estimated return for BAC, based on your analyst’s fundamental research is 15%. The stock is currently trading at $40.00 per share.

Would you choose to add BAC to a diversified portfolio according to CAPM? Why or why not?

A

Calculate “CAPM alpha”
For stock BAC:
* CAPM “Required” return: RBAC = 0.046 + 1.34(.11 -.046) = 0.1318 = 13.2%
* Estimated Return (using analyst’s expectations) = 15%
* Excess return or CAPM “alpha” = 15% - 13.2% = +1.80%

Yes, BAC would be a good addition to a well-diversified portfolio. It is expected to earn a positive alpha. i.e. it provides excess return for its systematic risk level (beta = 1.34)

38
Q

If BAC continues its current dividend payout ratio of approximately 2.60%, then
i) what is the expected one -year price based on CAPM?

A

Estimated capital gain according to CAPM: = 13.2% - 2.60% = 10.60%
–> P1CAPM = 1.106 x $40.00 = $44.24

39
Q

If BAC continues its current dividend payout ratio of approximately 2.60%, then
ii) What is the expected one-year price based on your analyst’s expectations?

A

Estimated capital gain according to your analyst: = 15.0% - 2.60% = 12.40%
–> P1ANALYST = 1.240 x $40.00 = $44.96

40
Q

What risks factors are captured by the CAPM model? Why is unsystematic risk not included in the CAPM?

A

CAPM is a single-factor model that determines a security’s required return based on its exposure to market risk, measured by beta (systematic risk).

It assumes that unsystematic risk can be eliminated by diversifying portfolios, so it doesn’t account for unsystematic risk.

41
Q

Consider the following multifactor model and two stocks: stock BAC and WMT, that have the following factor betas:

Bank of America:
Factor Beta 1 (GDP): 1.60
Factor Beta 2 (Inflation): -0.80

Walmart:
Factor Beta 1 (GDP): 0.60
Factor Beta 2 (Inflation): -0.20

Factor | Factor Risk Premium
GDP 4.0%
Inflation 1.5%

The zero-beta return (F0) = 4.50%.
Current stock prices are: BAC $40; WMT $60

Calculate the expected one-year returns for these two stocks, based on the APT model.

A

E(RBAC) = 0.045 + (1.6 x 0.04) + (-0.80 x 0.15) = 0.0970 = 9.70%
E(RWMT) = 0.045 + (0.6 x 0.04) + (-.20 x 0.15) = 0.0660 = 6.60%

42
Q

Consider the following multifactor model and two stocks: stock BAC and WMT, that have the following factor betas:

Ri = E(Ri) = F0 + βiGDP F1 + βiI F2 + ei

Bank of America:
Factor Beta 1 (GDP): 1.60
Factor Beta 2 (Inflation): -0.80

Walmart:
Factor Beta 1 (GDP): 0.60
Factor Beta 2 (Inflation): -0.20

Factor | Factor Risk Premium
GDP 4.0%
Inflation 1.5%

The zero-beta return (F0) = 4.50%.
Current stock prices are: BAC $40; WMT $60

Calculate the expected prices one year from now for both stocks, assuming that they do not pay dividends.

A

Expected (Required) price of BAC in 1 year (P1): = $40 x (1.097) = $43.88
Expected (Required) price of WMT in 1 year (P1): = $60 x (1.066) = $63.96

43
Q

Consider the following multifactor model and two stocks: stock BAC and WMT, that have the following factor betas:

Ri = E(Ri) = F0 + βiGDP F1 + βiI F2 + ei

Bank of America:
Factor Beta 1 (GDP): 1.60
Factor Beta 2 (Inflation): -0.80

Walmart:
Factor Beta 1 (GDP): 0.60
Factor Beta 2 (Inflation): -0.20

Factor | Factor Risk Premium
GDP 4.0%
Inflation 1.5%

The zero-beta return (F0) = 4.50%.
Current stock prices are: BAC $40; WMT $60

If your analyst (using several valuation methods) predicts that in one-year BAC will be $43/share and WMT will be $65/share, would you buy either, both, or none, based on the above factor model? (Assume no dividends are paid)

A

Est return for BAC = 43/40 – 1 = 7.50%
Est return for WMT =65/60 -1 = 8.33%

BAC APT = 9.70% < Estimated –> Sell
WMT APT = 6.60% > Estimated –> Buy

44
Q

With reference to APT, what is a zero-beta portfolio? What return should it earn?

A

A zero-beta portfolio is one that has no sensitivity to any macro factors (zero systematic risk) and can earn a return equal to the risk-free rate.

If it earns more than the risk-free rate, an arbitrage portfolio has been created.

45
Q

Suppose that two factors have been identified for the U.S. economy: the growth rate of industrial
production, IP, and the inflation rate, IR. IP is expected to be 3%, and IR 5%. A stock with a
beta of 1 on IP and .5 on IR currently is expected to provide a rate of return of 12%. If industrial
production actually grows by 5%, while the inflation rate turns out to be 8%, what is your revised
estimate of the expected rate of return on the stock?

A

Revised estimate = 12% + [(1 x 2%) + (.5 x 3%)] = 15.5%

46
Q

The APT itself does not provide guidance concerning the factors that one might expect to determine risk premiums. How should researchers decide which factors to investigate? Why, for example, is industrial production a reasonable factor to test for a risk premium?

A
  1. The APT factors must correlate with major sources of uncertainty, i.e., sources of uncertainty that are of concern to many investors. Researchers should investigate factors that correlate with uncertainty in consumption and investment opportunities. GDP, the inflation rate, and interest rates are among the factors that can be expected to determine risk premiums. In particular, industrial production (IP) is a good indicator of changes in the business cycle. Thus, IP is a candidate for a factor that is highly correlated with uncertainties that have to do with investment and consumption opportunities in the economy.
47
Q

Assume that both portfolios A and B are well diversified, that E ( rA ) 12%, and E ( rB ) 9%.
If the economy has only one factor, and A 1.2, whereas B .8, what must be the risk-free
rate?

A

12% = rf + (1.2 × RP)
9% = rf + (0.8 × RP)

Solving these equations, we obtain
rf = 3% and RP = 7.5%.

48
Q

pg 372. question 10

A

a. E(r) = 6% + (1.2 × 6%) + (0.5 × 8%) + (0.3 × 3%) = 18.1%

b. Unexpected return from macro factors =
[1.2 × (4% – 5%)] + [0.5 × (6% – 3%)] + [0.3 × (0% – 2%)] =–0.3%
E (r) =18.1% − 0.3% = 17.8%

49
Q

As a finance intern at Pork Products, Jennifer Wainwright’s assignment is to come up with fresh
insights concerning the firm’s cost of capital. She decides that this would be a good opportunity
to try out the new material on the APT that she learned last semester. She decides that three
promising factors would be (i) the return on a broad-based index such as the S&P 500; (ii) the
level of interest rates, as represented by the yield to maturity on 10-year Treasury bonds; and
(iii) the price of hogs, which are particularly important to her firm. Her plan is to find the beta
of Pork Products against each of these factors by using a multiple regression and to estimate the
risk premium associated with each exposure factor. Comment on Jennifer’s choice of factors.
Which are most promising with respect to the likely impact on her firm’s cost of capital? Can
you suggest improvements to her specification?

A

The first two factors seem promising with respect to the likely impact on the firm’s cost of capital. Both are macro factors that would elicit hedging demands across broad sectors of investors. The third factor, while important to Canola Products, is a poor choice for a multifactor SML because the price of canola is of minor importance to most investors and is therefore highly unlikely to be a priced risk factor. Better choices would focus on variables that investors in aggregate might find more important to their welfare. Examples include: inflation uncertainty, short-term interest-rate risk, energy price risk, or exchange rate risk. The important point here is that, in specifying a multifactor SML, we not confuse risk factors that are important to a particular investor with factors that are important to investors in general; only the latter are likely to command a risk premium in the capital markets.

50
Q

True or False and why?

Both the CAPM and APT require a mean-variance efficient market portfolio.

A

False

The CAPM requires a mean-variance efficient market portfolio, but APT does not.

51
Q

True or False and why?

Neither the CAPM nor APT assumes normally distributed security returns.

A

False

The CAPM assumes normally distributed security returns, but APT does not.

52
Q

True or False?

The CAPM assumes that one specific factor explains security returns but APT does not

A

True

53
Q

A zero-investment portfolio with a positive alpha could arise if

A

A risk-free arbitrage opportunity exists.

54
Q

According to the theory of arbitrage

A

Positive alpha investment opportunities will quickly disappear

55
Q

The arbitrage pricing theory (APT) differs from the single-factor capital asset pricing model
(CAPM) because the APT

A

Recognizes multiple systematic risk factors

56
Q

An investor takes as large a position as possible when an equilibrium price relationship is violated. This is an example of

A

Arbitrage activity.

57
Q

The feature of arbitrage pricing theory (APT) that offers the greatest potential advantage over
the simple CAPM is the

A

Use of several factors instead of a single market index to explain the risk–return
relationship

58
Q

In contrast to the capital asset pricing model, arbitrage pricing theory:

A

Does not require the restrictive assumptions concerning the market portfolio.

ADMS 4501 Midterm (5 decks)

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