Summer $2$Q$17$ examination

FM$429$ Asset Markets A

Suitable for all candidates

lnstructions to candidates

This paper contains three questions. Answe.r lwo questions.

All questions will be given equal weight $(50\%).$ Questions with parts have marks allocated as shown.

Time Alf owed Reading Time: $10$ minutes. You may po$!$ make notes during this time. Writing Time: t hour $30$ minutes.

You are supplied with: You may also use: Calculators:

No additional materials

No additional materials.

Calculators are allowed in this examination

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rHe LoNDotr$$ Scnool or ECoNoMICS nruo PoLITICAL ScIENcE r

$1.$ This question is about stock valuation and market efficiency $[50$ marks$]$

a$)[10$ marks$]$ The table below lists some partial information about a firm, fill in all missing values in the table:

Book equity

Earnings

Return on equ$$ty$,$ ROE Payout ratio

D$$vidends

Growth rate of dividends

$\mathrm{.}20202015$

$1010105050$

Year

$12345$

$100118$

$>=$$

b$)15$ marksl Assume that the expected return of the firm is constant at $10$o$/$o$,$ and the firm enters a constant growth phase after year $4($i$.$e$.,$ ROE and the payout ratio are constant thereafter$).$ Calculate the present value of the firm.

c$)[5$ marks$]$ What is the PVGO of the firm at the end of year $4($after the dividend payment$)?$

d$)15$ marksl Now assume that beginning in year $5,$ ROE drops to $10\%.$ What is the PVGO at the end of year $4($after the dividend $$ayment$)?$ Explain the intuition for your answer.

e$)[10$ marks$]$ Firms with high price$-$to$-$earnings $($P$/$E$)$ ratios tend to have had high earnings growth rates in the previous five years. lt is also well$-$known that these firms earn significantly negative abnorrnal returns in the subsequent three to five years. Does this evidence violate any form$($s$)$ of the efficient market hypothesis? What might be a potential explanation for this return pattern?

f$,)[8$ marks$]$ Some recent studies on the P$/$E ratio find that the return predictability is concentrated around subsequent earnings ahnouncement dates. For example, a firm with a high P$/$E ratio in April $2017$ is likely to have low stock returns around subsequent quarterly earnings announcements $($e$\mathrm{.}9.,$ in July and October $2017).$ What is a plausible $$nterpretation of this evidence?

g$)$ t$7$ marksl What are the potential market frictions$/$constraints that prevent arbitrageurs from taking advantage of the return pattern described $$n e$)?$ List two s uch frictions$/$constraints$.$

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$15$

$2.$ This question is about portfolio choice and the CAPM $[50$ marks$]$

Consider three portfolios of stocks, X$,$ Y$,$ and Z$,$ which have the following annual expected returns and standard deviations: E$[$rxl$=1$jo$/$o and ox$=20\%,$ E$[$rv$]=1$$$/$s and ov$=25$o$/$o$,$lrzl$=14$o$/$o and oz$=22$o$/$o$.$ The effective annual riskless rate is $5\%.$

a$)[5$ marks$]$ lt is known that one of the portfolios X$,$ Y$,$ Z lies on the efficient frontier $($which includes the riskless asset$).$ Which portfolio is efficient?

b$)[5$ marks$]$ Consider a conservative investor who wants to invest in a new portfolio P by allocating her wealth between the riskless asset and only one of the portfolios X$,$ Y$,$ or Z$.$ The investor wants her new portfolio to have a standard deviat$$on op $=10\%.$ What is the highest expected return that the investor can obtain?

c$)[10$ marks$]$ lt is known that portfolio Zis a combination of portfolios X and Y$,$ i$.$e$.$ rz $=$ wxrx $+(1-$w$)$xry$.$ What is the weight w$?$ What is the correlation between the returns of portfolios X and Y$?$

d$)[10$ marks$]$ Consider an investor who borrows $1,000$ and uses her own $2,000$ to invest $[2,000$ in portfolio X and $1,000$ in portfolio Y$.$ What is the expected return on the investor's portfolio? What is the standard deviation of the investor's portfolio?

e$)[5$ marks$]$ ls portfolio Zthe tangency portfolio? Why or why not?

$0[5$ marks$]$ What is diversification, and what are the limits to diversification? What types of risk can be diversified away, and what types cannot?

g$)[10$ marks$]$ Explain why the increase in portfolio variance when you add a small amount of a stock to your portfolio is largely determined by the stock's covariance with your portfolio.

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$3.$ This question is about futures, forwards and options $[50$ marks$]$

a$)$ A stock has a current price of $1,000.$ The term structure is flat at $1$o$/$o per year The stock will not pay any dividends over the next $3$ years.

$[5$ marks$]$What $$s the three$-$year forward price for the stock?

$[5$ marks$]$ lf the three$-$year fon$$vard price in the market for the stock is $1,035,$ is there an arbitrage opportunity? lf so$,$ how would you take advantage of it$?$

b$)[5$ marks$]$What are the main differences between futures and foruvard contracts?

c$)[10$ marks$]$ A stock has a current price of $90$ and will not pay any dividends in the next year. A European call on the stock with an exercise price of $100$ and a time to maturity of $6$ months has a price of $812.$ A European put on the stock w$$th an exercise price of $100$ and a time to maturity of $6$ months has a price of $15.$ The term structure is fl