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1Spring, 2017 ECON 445Quiz #1

Fill the blanks or choose the correct word. Each blank is worth 2 points unless specified otherwise.

[1] Financial assets are often classified into three major classes which are the fixed income securities, (i) and (ii).

Fixed income securities are called the fixed income (iii) market securities if the maturity is relatively short and

risk is very small, and called the fixed income (iv) market securities if the maturity is relatively long.

(i) (ii) (iii) (iv)

[2] A stock option is an example of one of the three major assets listed in [1]. An option is a contract whose value

is derived from the price of underlying asset. Options are traded in the market. When an option writer wants to

sell his contracts to someone else, or an investor wants to buy an option, the Options Clearing Corporation (OCC)

serves as an intermediary in the transaction. The option writer sells his contract to the OCC and the option buyer

buys it from the OCC.

The holder (buyer) of the put option has the (i), but no (ii), to (iii) a share of the underlying stock at a (iv) price on

or by the (v) date. The seller of the put option has the (vi) to (vii) the share if the holder (viii) the option. A put

option is out of money if the current market price is (ix) than the (x) price.

(i) (right, obligation) (ii) (right, obligation) (iii) (sell, buy) (iv)

(v) (vi) (right, obligation) (vii) (sell, buy) (viii)

(ix) (higher, lower) (x)

[3] If you sell a call option at the (i) price on the settlement date, you face two cases on the expiration date: the

buyer of your option either exercises the option or lets it expire. The buyer will exercise the call option only if the

call option is (ii) the money, that is, only if the market price is (iii) than the strike price. If the buyer lets the option

expire, your profit/loss is the price of the option you sold at. If the buyer exercises the call option, you buy a share

of stock in the market at the market price, deliver it to the buyer, and receive the (iv) price. Your net profit/loss is

equal to (v) price + (vi) price - (vii) price.

(i) (bid, ask) (ii) (in, out of) (iii) (lower, higher) (iv) (v) (bid, ask)

(vi) (vii)

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[4] John sells the shares of Walmart stock short at the current market price $69.49.

(a) Short sale means that you (i) shares of stock from a broker and sell them. The proceed is kept in your account.

You also have to put up (ii)% additional fund in the account, which is called the (iii) requirement.

(i) (ii) (iii)

(b) John plans to close his short sale account on February 13. He wants to protect his investment using a call

option. The call option of strike price $70 that expires on February 13 is traded at price $0.52 per share. Will he

buy this call option to protect from a higher price of $71? That is, will he buy the call option if he thinks the price

can rise to $71?

If he does not buy the call option and price rises to $71, his loss is $(i)-$(ii)=$(iii) per share. If he buys the call

option and exercises the option, he incurs $(iv) loss per share from the transaction of shares. Since he paid $(v)

per share for the option, his total loss will be $(vi). Therefore, his loss is (vii) when he buys and exercises the call

option.

(i) (ii) (iii) (iv) (v) (vi) (vii) (smaller, larger)

[5] The financial market plays four important roles in the economy: (i), consumption smoothing, (ii), and

separation of ownership and management. The benefit of the separation of ownership and management is that it

offers stability of the firm while its drawback is the (iii) problem. To avoid this problem, salaries of managers are

often tied to the profits of the company. This gives strong incentives to the managers to focus on the short-run

profits, and to falsify the profits. One example is the case of (iv) corporation whose managers moved debts into

(v) entities to make the corporation look more profitable. Another example is the telecommunication company

(vi). The managers of this company reported the (vii), which is the interconnection expense with other

telecommunication companies, as capital investment on the balance sheet.

(i) (ii) (iii) (iv)

(v) (vi) (vii)

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[1] 1(a) Major players in the financial market include households, firms, and federal and local governments. The

federal government issues Treasury (i), (ii) and bonds. Financial intermediaries include depositary banks,

investment companies and investment bankers. Investment companies pool the fund from many investors and

manage the funds for investors. Investment bankers specializes in the IPO, which stands for the (iii), in the

primary market of equities or bonds by “underwriting” new issues of securities. Underwriting means that a

syndicate of banks, who are called the lead managers, have taken on the risk of distributing the securities. If they

are unable to find enough investors, they will (iv). They offer advices on the price of the new security.

(i) (ii) (iii)

(iv) (return the unsold shares to the company, hold the unsold shares themselves)

(b) One of the recent trend in the financial market is the globalization. If U.S. investors want to invest in foreign

companies, they can buy ADR, which stands for (i), instead of buying the shares of foreign companies whose

prices in dollars are subject to the (ii) risk. To overcome this, a broker purchases a block of foreign shares,

deposits them in a trust and issues ADRs in the U.S. They are traded in (iii) in the US market, receive dividends in

(iv). The WEBS, which stands for the World Equity Benchmark Shares, are the same as ADRs, but are for

portfolios of stocks.

(i) (ii) (iii) (dollars, foreign currency)

(iv) (dollars, foreign currency)

(c) Securitization is the process of creating securities by pooling together various financial assets that generate (i).

Examples of such financial assets are (ii), student loans, auto loans, and etc. These securities are then sold to the

investors. One of the important securities is the MBS, which stands for the (iii) and played a significant role in the

recent financial crisis.

(i) (ii) (iii)

1(d) Fixed income money market securities include the Treasury (i), certificate of deposits, commercial paper,

Eurodollars, federal funds, and etc. The Eurodollar is the (ii) denominated deposits held (iii) the U.S. The time

deposits denominated in Euro and held outside of Euro zone is called the (iv). Federal fund is the fund in the

account of depository institutions such as commercial banks at the Federal Reserve Bank to meet the (v) reserve.

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When a bank does not have a sufficient reserve, it borrows from another bank overnight. The interest rate on such

a loan is called the (vi) rate.

(i) (ii) (Dollar, Euro) (iii) (outside, inside) (iv) (v)

(vi)

(e) The LIBOR stands for (i) and it was a benchmark rate that some of the world’s leading banks charge each

other for unsecured short-term loans. It used be administered by the British Bankers’ Association (BBA), which

set the rates for (ii) major world currencies with 15 maturities for each currency based on the survey of member

banks. It was revealed in recent years that some member banks submitted a rate that is lower than the rate they

can borrow. One of them was the British bank (Barclays) which was holding a large amount of the IRS which

stands for the (iii). This scandal led to a reform of the LIBOR. The new LIBOR is called the ICE LIBOR where

ICE stands for the (iv). It now sets the rates for (v) major currencies with (vi) maturities for each currency. The

currencies included in ICE LIBOR are US dollars, Pound Sterling, Euro, (vii) and Swiss Francs.

(i) (ii) (iii)

(iv) (v) (vi) (vii)

1(f) Prime examples of fixed income capital market securities are the Treasury notes and bonds, which pay

interest every (i) months until they mature. The interest rate on these securities are called the (ii) rate. The

Treasury notes have maturities of 2, 3, (iii), (iv) and 10 years. TIPS stands for (v). The coupon rate of TIPS is (vi)

over time. Their face value is adjusted by the (vii) every (viii) months.

(i) (ii) (iii) (iv) (v)

(vi) (fixed, adjusted) (vii) (viii)

[2] (a) Treasury Bills are sold through public Dutch auction at a (i) value of the (ii) value. The maturities of T-

bills are 4, 13, (iii), (iv) weeks.

(i) (ii) (iii) (iv)

(b) The bid price of the T-bill is the price that an investor (i) from brokers when she (ii) the T-bill, and the asked

price is price that an investor (iii) when she (iv) the T-bill.

(i) (receives, pays) (ii) (sells, buys) (iii) (receives, pays) (iv) (sells, buys)

(c) The online WSJ reports daily data on the T-Bills as follows

Friday, February 10, 2017

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Maturity Bid Asked Chg Asked yield

5/18/2017 0.525 0.515 0.010 0.523

The date February 10, 2017 is called the settlement date. The date under Maturity is the date when you receive the

(i) value if you hold the bill till the maturity date. The number under “Bid” represents the annualized (ii) rate

based on the bid price, the number under “Asked” represents the annualized (iii) rate based on the asked price,

and the number under “Asked yield” represents the annualized (iv) yield based on the asked price. The number

under “Chg” represents the change in the number under Bid from previous trading day.

(i) (ii) (iii) (iv)

(d) Let FV and P denote the face value and the asked price of a Bill, respectively. How do you compute the bank

discount rate r BD and the bond equivalent yield r BE over the holding period from the settlement date to the

maturity date. Write the formulas. (4 point each)

r BD=¿ r BE=¿

1(e) Let DSM be the number of days from the settlement date to maturity. Write the formulas for the annualized

bank discount rate rABD, the annualized bond equivalent yield r ABE, and the annualized money market yield

r AMM . (4 point each)

rABD=¿ rABE=¿ r AMM=¿

1(f) Suppose you know the FV, DSM and r ABD. Derive the equation for price from the equation for r ABD you

wrote in question (e). Show your work. (6 points)

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[1] 1The Eurodollar bond is denominated in (i) and it is issued by a (ii) entity (iii) the U.S. Companies of another

country may want to issue bonds in the US in denomination of US dollars. This bond is called the (iv) bond. If

non-Australian entity issues a bond denominated in Australian dollars in Australia, it is called a (v) bond.

(i) (U.S. dollar, Euro) (ii) (nonU.S., U.S.) (iii) (inside, outside) (iv) (v)

[2] The following table shows an example of market data on Treasury note with face value $100.

Friday, February 24, 2017Maturity Coupon Bid Asked Chg Asked

yield

5/15/2017 0.875 100.0391 100.0547 -0.0313 0.617What does the number under each heading represent? The Coupon column represents the fixed (i) interest rate of

the note in percentage; the Bid column shows the price at which an investor can (ii) the note; the Asked column

shows the price at which an investor can (iii) the note; and the Asked yield shows the annualized (iv) yield of the

note if you buy the note and hold it till maturity.

(i) (annual, semiannual) (ii) (buy, sell) (iii) (buy, sell) (iv) (percentage, decimal)

[3] Local governments usually issue bonds at a fixed interest rate. But, some local governments issued them at a

floating rate and then entered the IRS agreement with the banks, where the IRS stands for the (i).

(i)

To understand how the IRS works, consider two firms, A and B. Firm A wants a floating rate loan because it

expects the interest rate will decline while firm B wants a fixed rate loan because it expects a rise in interest rate.

The current interest rate they face in the market are as follows.

firm fixed floating

A 5% LIBOR+0.3%

B 6% LIBOR+0.9%

(a) Firm B has to pay a higher interest rate than firm A in either market. But, firm B has a comparative advantage

in the (i) interest rate market. Therefore, they agree on an IRS, in which firm B borrows a (ii) rate loan and firm A

borrows a (iii) rate loan. Firm A agrees to pay a floating rate LIBOR+0.2% to firm B and firm B pays a fixed rate

x% to firm A. We need to determine x that benefits both firms. To do this, we need to figure out the net interest

rate each firm pays when they sign on the IRS. The net rate that firm A has to pay is (iv) and the net rate that firm

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B has to pay is (v).

(i) (floating, fixed) (ii) (floating, fixed) (iii) (floating, fixed)

(iv) (v) (4 points each for (iv) and (v))

(b) Each firm's net interest rate must be lower than what each firm can borrow their preferred loans. This requires

that firm A’s net rate must be lower than LIBOR+0.3% and firm B's nest rate must be lower than 6%. These two

conditions require that x% must be greater than (i) and less than (ii). If x% is closer to the lower bound, firm B is

better off than firm A. Suppose we choose a fair split by taking the average of the two bounds. Then, x=(iii), and

the net interest rate for firm A is (iv) and the net interest rate for firm B is (v). These results show that both firms

are better off.

(i) (ii) (iii) (iv) (v)

[4] An example of equity securities is the common stock. It represents a share of ownership of the company and

they are traded in stock markets. The largest stock markets in the U.S. are the (i) stock exchange, American stock

exchange, and the NASDAQ which stands for the (ii). There are many stock market indexes that represent the

overall performance of various stocks. Three major market indexes are the Dow Jones Industrial Average (DJIA),

the S&P 500 composite index, and the NASDAQ composite index. The DJIA index is a (iii) weighted index of

(iv) blue chip companies. The S&P500 index and the NASDAQ index are the (v) weighted index of 500 large cap

companies and all stocks registered at the NASDAQ market, respectively.

(i) (ii)

(iii) (price, market capitalization, equally) (iv) (30, 100, 500) (v) (price, market capitalization, equally)

[5] You have $12,000 to invest in two stocks: ABC and XYZ. You wish to track the price-weighted (PW) index,

or the market value weighted (VW) index, or equally weighted (EW) index. Consider information in the

following table.

stocks #outstanding

shares (mil)

Initial

Price

value of

firm

PW VW EW

amount shares amount shares amount shares

ABC 20 25 500

XYZ 4 75 300

value of account 12,000 NA 12,000 NA 12,000 NA

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(a) To track these indexes, you need to allocate the fund in a certain way. Write the fraction of fund to be invested

in ABC stock for each index. (note: write fractions in the form of 2/5, for example)

PW index: VW index: EW index:

(b) Fill in the amount of fund to be invested in each stock and shares of each stock for each index.

(10 points all-or-none for the entire table)

(c) Suppose that the price of ABC decreased to $20 and the price of XYZ increased to $80. Evaluate each account

and fill in the empty cells in the table below. (10 points all-or-none for the entire table)

stocks #outstanding

shares (mil)

new

price

value of

firm

PW VW EW

amount shares amount shares amount shares

ABC 20 20 400

XYZ 4 80 320

value of account NA NA NA

(d) After price changes, the ratio of investment amount between ABC and XYZ is (i) to the ratio of (ii) in the PW

account and it is (iii) to the ratio of (iv) in the VW account. The allocation of new balance of EW account after

price changes does not conform the EW index property because the investment amounts are not equal. To

rebalance the account, you need to move $(v) from XYZ to ABC. You can do this by selling (vi) shares of XYZ

and buy (vii) shares of ABC.

(i) (equal, not equal) (ii) (prices, market capitalization) (iii) (equal, not equal)

(iv) (prices, market capitalization) (v) (vi) (vii)

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1Spring, 2017 ECON 445Midterm Exam


[1] (a) The federal government issues Treasury (i), notes and bonds. Investment (ii) pool the fund from many

investors and manage the funds for investors, and investment (companies, bankers) specialize in the IPO, which

stands for the (iii).

(i) (ii) (companies, bankers) (iii) (companies, bankers) (iv)

(b) Securitization is the process of creating securities by pooling together various financial assets that generate (i).

When the underlying assets are mortgages, the securities are called the (ii).

(i) (ii)

(c) The Eurodollar is the (i) denominated deposits held (ii) the U.S. The time deposits denominated in Euro and

held outside of Euro zone is called the (iii). Federal fund is the fund in the account of depository institutions such

as commercial banks at the Federal Reserve Bank to meet the (iv) reserve. When a bank does not have a sufficient

reserve, it borrows from another bank overnight. The interest rate on such a loan is called the (v) rate.

(i) (US Dollar, Euro) (ii) (outside, inside) (iii) (iv) (v)

(d) The online WSJ reports daily data on the T-Bills. The current date is called the settlement date. The date under

"Maturity" is the date when you receive the face value if you hold the bill till the maturity date. The number under

“Bid” and "Asked" represent the annualized (i) rate based on the bid and asked price, respectively, and the

number under “Asked yield” represents the annualized (ii) yield based on the asked price.

(i) (bank discount, bond equivalent) (ii) (bank discount, bond equivalent)

(e) Let FV and P denote the face value and the asked price of a Bill, respectively. The bank discount rate r BD and

the bond equivalent yield r BE over the holding period from the settlement date to the maturity date are computed

by

r BD=¿ r BE=¿

1(f) Let DSM be the number of days from the settlement date to maturity. The annualized bank discount rate r ABD

, the annualized bond equivalent yield r ABE, and the annualized money market yield r AMM are computed by

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r ABD=rBD×( )

DSM r ABE=rBE×

( )DSM

rAMM=r BE×( )

DSM

(g) Daily report of stocks of Wall Street Journal includes several columns. The column under "Close" shows the

closing price, the "DIV" column shows the annualized last (i) dividend, the "P/E" shows the (ii)-to-(iii) ratio

which is the current price/last year’s earnings per share, the "Yield" shows the annualized (iv)/current price, and

"YTD%CHG" represents the percentage change in price from the (v) of the year to today.

(i) (quarterly, semiannual) (ii) (iii) (iv) (v)

[2] A stock option is an example of an asset called (i) whose values are derived from the price of underlying

assets. Options are traded in the market. When an option writer wants to sell his contracts to someone else, or an

investor wants to buy an option, the OCC serves as an intermediary in the transaction, where OCC stands for (ii)

Corporation. The option writer sells his contract to the OCC and the option buyer buys it from the OCC. The

holder of a call option has the (iii), but no (iv), to (v) a share of the underlying stock at a (vi) price on or by the

(vii) date. A call option is in the money if the current market price is (viii) than the (ix) price.

(i) (ii) (iii) (right, obligation) (iv) (right, obligation)

(v) (sell, buy) (vi) (vii) (viii) (higher, lower)

(ix)

[3] Consider two firms, A and B. Firm A wants a floating rate loan because it expects the interest rate will decline

while firm B wants a fixed rate loan because it expects a rise in interest rate. The current interest rate they face in

the market are as follows.

firm fixed floating

A 5% LIBOR+0.3%

B 6% LIBOR+0.9%

(a) Firm B has to pay a higher interest rate than firm A in both the fixed rate loan and floating rate loan markets.

But, firm B has a comparative advantage in the (i) interest rate market because it has to pay 0.6% more interest

rate than firm A in the floating rate market while it has to pay 1% more interest rate than firm A in the fixed rate

loan market. Therefore, they agree on an IRS, in which firm B borrows a (ii) rate loan and firm A borrows a (iii)

rate loan. Firm A agrees to pay a floating rate LIBOR+x% to firm B and firm B pays a fixed rate 5.8% to firm A.

We need to determine x that benefits both firms. To do this, we need to figure out the net interest rate each firm

pays when they sign on the IRS.

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Firm A

pays (iv)% to the lender

pays LIBOR+x% to firm B

receives 5.8% from firm B

Net rate = (v) - 5.8% = (vi)

Firm B

pays (vii) to the lender

pays 5.8% to firm A

receives LIBOR+x% from firm A

Net rate=(viii)-(ix)=(x)


(iv) (v) (vi) (vii)

(viii) (ix) (x)

(b) Each firm's net interest rate must be lower than what each firm can borrow their preferred loans directly in the

market. This requires that firm A’s net rate must be lower than LIBOR+0.3% and firm B's net rate must be lower

than 6%. These two conditions require that x% must be greater than (i) and less than (ii). If x% is closer to the

upper bound, firm (iii) gets more benefit than firm (iv). Suppose they agree to a fair split by taking the average of

the two bounds. Then, x=(v), and the net interest rate for firm A is (iv) and the net interest rate for firm B is (v).

These results show that both firms are better off.

(i) (ii) (iii) (iv) (v) (iv) (v)

[4] The Dow Jones Industrial Average (DJIA) index is essentially an average of stock prices of 30 blue chip

companies. The companies included in the index are replaced with other companies from time to time. If the stock

price of exiting company is different from the stock price of new company, the DJIA index will change. This is an

undesirable property because such a change does not reflect the change of overall market. To avoid it, the DJIA

index uses (i). For example, consider two companies ABC and XYZ whose share prices are $30 and $90,

respectively. The DJIA index is the average of these two prices, i.e., index=(30+90)/2=60. Now, suppose that

XYZ is replaced with DEF whose stock price is $150. Compute the value of the item you specified in (i) above.

(i) (ii)

[5] You have $12,000 to invest in two stocks: ABC and XYZ. You wish to track the price-weighted (PW) index,

or the market value (market capitalization) weighted (VW) index, or equally weighted (EW) index. Consider

information in the following table.

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stocks #outstanding shares

Initial New

price marketvalue

price market value

ABC 200 20 4,000 25 5,000

XYZ 100 80 8,000 75 7,500

(a) To track these indexes, you need to allocate the fund in a certain way. The fraction of fund to be invested in

ABC stock at initial prices is (i) for PW index, (ii) for VW index and (iii) for EW index. These fractions indicate

that the amount of fund to be invested in ABC stock at initial prices is $(iv) for PW, $(v) for VW and $(vi) for

EW. (note: write fractions in the form of 2/5, for example)

(b) At new prices, the fraction of fund to be invested in ABC stock is (vii) for PW, (viii) for VW and (ix) for EW.

To check whether you have to reallocate your fund to track each index, you compute the values of your holdings

at new prices, and compute the fractions of investment in ABC stock. The resulting faction for (x) account does

not match with the fraction you found in questions (vii), (viii) and (ix) above.

(c) This means that, when prices change, you need to rebalance fund allocation in (xi) account.

(i) (ii) (iii) (iv) (v) (vi)

(vii) (viii) (ix) (x) (PW, VW, EW) (xi) (PW, VW, EW)

[6] 1You can invest in a risk-free asset and/or a risky asset. The probabilities of states and returns in each state are

shown in the table below, where 1w is the fraction of investment on risky asset, and rp, rf and rc denote returns of

risky asset, risk-free asset, and complete portfolio, respectively.

states p(s)

Return(s) (%) Complete portfolio

risky asset (rp)

risk-free asset (rf)

w=3/4

rc(s) [rc(s)-E(rc)]2

good 0.2 4 1

normal 0.6 2 1

bad 0.2 0 1

(a) Verify that E(rp)=2 and σ p2=1.6. Show your work.(4 points each)

E(rp)=

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σ p2=

(b) Fill in the blank cells under rc(s) of complete portfolio when w=3/4, and compute E(rc) using those numbers.

Show your work.

E(rc)=

(c) Fill in the blank cells under [rc(s)-E(rc)]2 and compute σ c2 using those numbers. Show your work.

σ c2 =

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[1] 1 You have two choices in allocating your investment fund: a risk-free asset and a risky asset. Let r f and r p be

returns of the risk-free asset and risky asset, respectively. Let μp=E(r p) and σ p2=var (r p). Let w be the fraction

of fund to be invested in the risky asset.

(a) The return rc of the complete portfolio can be written as

rc=¿

The expected value μc=E (rc) is

μc=(1−w )r f+()=rf+()

Show that the variance of rc is σ c2=w2σ p

2. (4 points)

σ c2=E (rc−μc)

2=¿

(b) The investor is concerned only about the expected return μc and the risk σ c of the complete portfolio in their

decision on w. The figure below shows the choice set, i.e., all combinations of the expected return and risk that an

investor faces as she chooses different values of w. This line is called the CAL which stands for the (

). The slope of the CAL is called the ( ) ratio. It represents the additional ( ) that the

investor can gain as she takes one more unit of risk. Mark the points on the CAL for w=0, w=1, and w=0.5, and

write the value of w for each point.

ER (μc)

μp

μf

σ prisk (σ c)

(i) (ii)

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(c) Derive the equation for the CAL. (4 points)

(d) Given the CAL, the optimal choice of w depends on investor's preference over the expected return and risk.

Investor's attitude toward risk can be classified into three classes: risk averse, risk neutral and risk loving. To

define these terms, consider an agent who faces two choices: receive cash of $600 or receive a lottery which pays

$200 or $1,000 with an equal probability. A risk averse agent prefers (cash, lottery), a risk loving agent prefers

(cash, lottery), and a risk neutral agent is indifferent between the two choices. Suppose you hold the lottery. If you

are risk averse, this lottery is worth ($600, less than $600, more than $600) for you. The minimum price that you

are willing to sell this lottery is called the ( ) value of the lottery.

(e) An indifference curve in the risk and expected return space represents all combinations of risk and expected

return that give the same level of utility. Indifference curves slope (upward, downward, flat) for a risk averse

agent, and indifference curves slope (upward, downward, flat) for a risk loving agent, and indifference curves for

a risk neutral agent slope (upward, downward, flat).

(f) A risk averse agent's. indifference curve may exhibit increasing, decreasing and constant marginal rate of

substitution (MRS) of risk for expected return. Consider an agent whose indifference curve has an increasing

MRS. Show in the figures below that this agent (i) can be a diversifier (w is between 0 and 1) or (ii) can be a

plunger into risky asset only (w=1). You need to draw appropriate indifference curve in each figure.

ER (μc)

risk (σ c)

μf

μp

σ p

CAL

ER (μc)

risk (σ c)

μf

μp

σ p

CAL

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[2] Consider the choice set of expected return and risk when two risky assets are available. Let ri, μi, and σ i2 be

the return, expected return and variance of risky asset i, respectively, i=1,2, and let σ 12 and ρ be the covariance

and correlation coefficient between risky assets. . We construct a portfolio by investing w i fraction of fund on

asset i, where w1+w2=1. The curve in the risk and expected return space that represents all pairs of risk and

expected return that are attainable by changing w i is called the PPC which stands for the (portfolio possibility curve). To compute the PPC, we need to compute the return, expected return and variance of portfolio which are

denoted by r p, μp, and σ p2, respectively.

(a) Write r p and μp

r p=¿

μp=E ( r p )=¿

σ p2 = (w1σ1 )2+ (w2σ 2)2+2w1w2σ12 = (w1σ1 )2+ (w2σ 2)2+2 ρ(w¿¿1σ1)(w2σ2)¿

(b) Show that the PPC is a straight line in the case of ρ=1. (6 points)

(d) Consider the case of ρ=-1. Derive the value of w1 for which σ p=0. (6 points)

17






asset i, where w1+w2=1. The curve in the risk and expected return space that represents all pairs of risk and

expected return that are attainable by changing w i is called the PPC which stands for the ( ). To compute the PPC, we need to compute the return, expected return and variance of portfolio which are

denoted by r p, μp, and σ p2, respectively. Consider the PPC in the following figure.

(a) The return of risk-free asset is 0.5. Draw the optimal CAL in the figure and indicate the optimum portfolio P. (4 points) (b) Indicate the diversifying risk averse agent's optimum complete portfolio on the optimum CAL.

2.50 3.00 3.50 4.00 4.50 5.00 5.500.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

[2] A single-index model specifies that the excess return Ri=r i-r f of a risky asset i is determined by two risk

factors: a common factor that affects all stocks and a firm specific factor that affects only one firm. This

relationship is written as

Ri=αi+β iRm+ei

18

where all notations are as used in the lecture. Let μi=E (Ri), μm=E(Rm), and σ i2, σ m

2 and σ ei2 denote the

variances of Ri, Rm and e i, respectively. The index model makes the following assumptions:

(A1) E (e i|Rm )=¿

(A2) (Ri ,Rm) are ( ) and ( ) distributed

(a) Assumption (A1) implies that firm specific shocks e i have zero expected values and it also implies that e i (are,

are not) correlated with the excess return of the market portfolio. (A2) implies that firm specific shocks e i (are, are

not) correlated with each other.

(b) Assumption (A1) implies the conditional and unconditional means of Ri as given below:

(i) E (Ri|Rm )=¿ (ii) E(R i)=¿

Under assumptions (A1) and (A2), show that the variance of Ri is σ i2=β i

2σ m2 +σe i

2 . (4 points)

(iii) σ i2=E (Ri−μi )

2=¿

(c) β i is called the "beta" of asset i and it represents the marginal effect of a change in Rm on Ri or on E (Ri|Rm ). The equation in (i) of question (b) above indicates that, given the market excess return Rm, the expected excess return of asset i is the sum of two components. One component that is attributable to the market condition as a whole is equal to ( ), and another component is the ( ) of asset i and it represents the expected excess return of stock i beyond any return induced by market’s excess return. (d) Equation (iii) in question (b) shows two components in the risk (volatility) of Ri. The risk of asset i

attributable to the uncertainty common to the entire market is the term (β i2σm

2 , σ ei2) and it is called the (systematic,

non-systematic) risk, and the risk from the changes in the firm-specific factor is the term (β i2σm

2 , σ ei2) and it is

called the (systematic, non-systematic) risk. The former is also called the (market, firm specific) risk and the latter is also called the (market, firm specific) risk. The risk that can be removed by diversification is the (market, firm specific) risk.(e) If β i>1, the return of asset i is (less, more) volatile and it is (riskier, safer) than the market as a whole. The converse holds when the beta of asset i is less than 1. The beta of Walmart is expected to be (greater, smaller) than 1 and the beta of Bank of America is expected to be (greater, smaller) than 1. Do you think the beta of Google is much greater than 1, or much less than 1, or around 1? Present your argument.

Answer:

[3] Work out the Excel part of Quiz5 posted on the class website and send the file to the TA([email protected]) by 5 p.m. tomorrow (4/28/2017).

mailto:[email protected]

20



[1] Consider a single-index model

Ri=αi+β iRm+eiwhere all notations are as used in the lecture. The index model makes the following assumptions:

(A1) E (e i|Rm )=0 ⇒ E(ei)=0

(A2) (Ri ,Rm) are independently and identically distributed

We wish to construct a PPC using the single index model. To do this, we need to compute expected values,

variances and covariances across assets.

(i) μi=E (Ri)=α i+ βi μm (ii) σ i2=var (Ri)=βi

2σ m2 +σe i

2

(a) Show (4 points each)

(iii) σ ij=cov (R i , R j )=β i β j σm2

(iv) σ ℑ=cov (Ri ,Rm )=β i σm2

[2] Parameters of the single index model are estimated by the ordinary least squares (OLS) method. This method

find α i and β i that minimizes the sum of squared residuals (SSR) which is defined as

SSRi=¿

where T is the number of sample for each asset. Let α i and β i be the OLS estimators and let R¿=α i+ βi Rmt be the

predicted values and e¿=R ¿−R ¿ be the regression residuals. μm=E(Rm) and σ m2 =var (Rm) are computed by the

sample mean and sample variance of Rm. σ ei2=var (ei) is computed by

σ ei2=¿

Other parameters are then computed from (i)-(iv) by replacing parameters with their estimates.

21

[3] Using estimated parameters in computing the PPC and optimum portfolio assumes that the parameter values in the investment period are the same as those in the sample period. However, they may not stay constant over time. It has been observed empirically that betas tend to converge toward the average of betas of all equities, which is 1.

This property is called the mean reversion property. Merrill Lynch incorporates this property into the computation

of beta by taking a weighted average of estimated historical beta ( β ¿ and 1:

Adjusted beta βadj =

[4] An alternative way to take changing beta into account is the method that Blume developed. Blume’s idea is to

find the common trend of betas over time and use the trend to predict the betas in forecasting period. Explain the

steps to follow to execute Blume’s method.

(i) Select two ( ) periods, period 1 and period 2.

(ii) Estimate the beta of each stock in each period separately. Let them be denoted by β i1 and β i2 for each stock

i=1,2,,N.

(iii) The common time trend between these two sets of estimates is modeled as a linear regression model with

intercept δ and slope γ and it is specified as

β i2=, i=1,2 ,⋯ , N

Let the estimates of intercept and slope terms be denoted by δ and γ, respectively.

(iv) Forecast (estimate) the beta in investment period (period 3) by

β i3=¿

[5] The least square estimator of alpha and beta in the index model treats all observations equally. That is, recent

data and old data are not differentiated. As we try to forecast their values in the near future, it is intuitively

appealing to give more weights on recent data than on the data in the distant past. This can be done using the

Exponentially Weighted Average estimator.

(a) Let Z1, Z2, ⋯, ZT be a sequence of data of size T, where Z1 is the oldest data and ZT is the most recent data.

The weighted average with weights w t for Zt is

Z=∑t=1

T

w tZ t, ∑t=1

T

wt=1

The equally weighted average uses w t=() and the exponentially weighted average uses

22

w t=¿

where λ is a number between ( ) and ( ).

(b) The OLS estimator is given by

β i=∑t=1

T

(R ¿−R i)(Rmt−Rm)

∑t=1

T

(Rmt−Rm)2

This estimator can be considered as the ratio of equally weighted averages. The exponentially weighted estimator

of beta is then written as

β i=¿

[6] Work out the Excel part of Quiz 6 posted on the class website and send the file to the TA([email protected]) by 5 p.m. tomorrow (4/28/2017).

mailto:[email protected]

23

1Spring, 2017 ECON 445Final Exam


[1] An option is a contract whose value is derived from the price of underlying asset. The holder (buyer) of the

put option has the (i), but no (ii), to (iii) a share of the underlying stock at a (iv) price on or by the (v) date. A put

option is out of money if the current market price is (vi) than the (vii) price.

(i) (right, obligation) (ii) (right, obligation) (iii) (sell, buy) (iv)

(v) expiration (vi) (higher, lower) (vii)

[2] John sells the shares of Walmart stock short at the current market price $69.49. John plans to close his short

sale account on June 30. He wants to protect his investment using a call option. The call option of strike price $70

that expires on June 30 is traded at price $0.52 per share. Will he buy this call option to protect from a higher

price of $71? That is, will he buy the call option if he thinks the price can rise to $71? If he does not buy the call

option and price rises to $71, his loss is $(i)-$(ii)=$(iii) per share. If he buys the call option and exercises the

option, he incurs $(iv) loss per share from the transaction of shares. Since he paid $(v) per share for the option, his

total loss will be $(vi). Therefore, his loss is (vii) when he buys and exercises the call option.

(i) (ii) (iii) (iv) (v) (vi) (vii) (smaller, larger)

[3] (a) The MBS is one of the important securities that are created by pooling together various financial assets that

generate cash flows. The MBS stands for the (i) and it is funded mostly by (ii).

(i) (ii)

(b) After the scandal of manipulating the LIBOR, it was reorganized and changed its name to the ICE LIBOR

where ICE stands for the (i). It now sets the rates for (ii) major currencies with (iii) maturities for each currency.

The currencies included in ICE LIBOR are US dollars, Pound Sterling, Euro, Yen and (iv).

(i) (ii) (iii) (iv)

(c) The online WSJ reports daily data on the T-Bills as follows

Friday, February 10, 2017

Maturity Bid Asked Chg Asked yield

5/18/2017 0.525 0.515 0.010 0.523

24

The number under “Bid” represents the annualized (i) rate based on the bid price, and the number under “Asked

yield” represents the annualized (ii) yield based on the asked price.

(i) (ii)

(d) Let FV and P denote the face value and the asked price of a Treasury Bill, respectively. How do you compute

the bank discount rate rBD and the bond equivalent yield rBE over the holding period from the settlement date to

the maturity date. Write the formulas. (4 point each)

r BD=¿ r BE=¿

1(e) Let DSM be the number of days from the settlement date to maturity. Write the formulas for the annualized

bank discount rate r ABD, the annualized bond equivalent yield r ABE, and the annualized money market yield r AMM. (4 points each)

r ABD=¿ r ABE=¿ r AMM=¿

[4] Consider two firms, A and B. Firm A wants a floating rate loan because it expects the interest rate will decline

while firm B wants a fixed rate loan because it expects a rise in interest rate. The current interest rate they face in

the market are as follows.

firm fixed floating

A 5% LIBOR+0.3%

B 6% LIBOR+0.9%

(a) Firm B has to pay a higher interest rate than firm A in either market. But, firm B has a comparative advantage

in the (i) interest rate market. Therefore, they agree on an IRS, in which firm B borrows a (ii) rate loan and firm A

borrows a (iii) rate loan. Firm A agrees to pay a floating rate LIBOR+0.2% to firm B and firm B pays a fixed rate

x% to firm A. We need to determine x that benefits both firms. To do this, we need to figure out the net interest

rate each firm pays when they sign on the IRS. The net rate that firm A has to pay is (iv) and the net rate that firm

B has to pay is (v).


(iv) (v) (4 points each for (iv) and (v))

(b) Each firm's net interest rate must be lower than what each firm can borrow their preferred loans. This requires

that firm A’s net rate must be lower than LIBOR+0.3% and firm B's nest rate must be lower than 6%. These two

conditions require that x% must be greater than (i) and less than (ii). If x% is closer to the lower bound, firm B is

25

better off than firm A. Suppose we choose a fair split by taking the average of the two bounds. Then, x=(iii), and

the net interest rate for firm A is (iv) and the net interest rate for firm B is (v). These results show that both firms

are better off.

(i) (ii) (iii) (iv) (v)

[5] (a) Three major stock market indexes are the Dow Jones Industrial Average (DJIA), the S&P 500 composite

index, and the NASDAQ composite index. The DJIA index is a (i) weighted index of (ii) blue chip companies.

The S&P500 index and the NASDAQ index are the (iii) weighted index of 500 large cap companies and all stocks

registered at the NASDAQ market, respectively.

(i) (price, market capitalization, equally) (ii) (30, 100, 500) (iii) (price, market capitalization, equally)

(b) You have $24,000 to invest in two stocks: ABC and XYZ. The share prices of ABC and XYZ are $25 and

$75, respectively, and their outstanding shares are 20 million and 4 million, respectively.

(i) If you want to track the DJIA index, how do you allocate your fund? Show your work.

ABC: XYZ:

(ii) If you want track the S&P500 composite index, how do you allocate your fund? Show your work.

Value of firms are $500 million for ABC and $300 for XYZ. Therefore,

ABC: XYZ:

(c) ABC took a reverse stock split of one for two, i.e., stock holders receive one new stock for two old stocks they

hold. The share price of the new stock is doubled to $50. How do you rebalance your investment accounts? Show

your work.

(i) DJIA account

ABC: XYZ:

(ii) S&P500 account

ABC: XYZ:

[6] (a) An agent faces two choices: receive cash of $550 or receive a lottery which pays $400 or $1,000 with

probability 3/4 and 1/4, respectively. A risk averse agent prefers (i), a risk loving agent prefers (ii), and a risk

neutral agent is indifferent between the two choices. Suppose you hold the lottery. If you are risk averse, this

lottery is worth (iii) for you. The minimum price that you are willing to sell this lottery is called the (iv) value of

the lottery.

(i) (cash, lottery) (ii) (cash, lottery) (iii) ($550, less than $550, more than $550) (iv)

risk

ER

A

CB

D

P1

26

(b) Suppose a risk averse agent has a portfolio P1. To explain the indifference curve of this agent, consider

the figure below.

Can we find a portfolio in quadrant A that can be indifferent to P1? The answer is (i) because any portfolio

in that quadrant has a (ii) expected return and has a (iii) risk than P1. Therefore, the agent prefers (iv). A

similar line of thought indicates that the risk averse agent prefers (v). Can we find a portfolio in quadrant B

that can be indifferent to P1? The answer is (vi) because any portfolio in that quadrant has a (vii) expected return

and has a (viii) risk than P1. Therefore, a portfolio in that quadrant (ix) give the same utility. A similar logic

can apply to a portfolio in quadrant D. These considerations lead us to conclude that the indifference curve of a

risk averse agent has sloped (x).

(i) (no, yes) (ii) (higher, lower) (iii) (greater, smaller) (iv) (P1, a portfolio in A)

(v) (P1, a portfolio in C) (vi) (no, yes) (vii) (higher, lower) (viii) (greater, smaller)

(ix) (can, cannot) (x) (downward, upward)




asset i, where w1+w2=1. All pairs of risk and expected return that are attainable by changing w i in the risk and expected return space is called the PPC. (a) To compute the PPC, we need to compute the return, expected return and variance of portfolio which are

denoted by r p, μp, and σ p2, respectively. It is easy to show r p=w1 r1+w2r2, μp=w1 μ1+w2 μ2, and σ p

2 is (i).

(b) Let the risk free return is denoted by r f . The complete portfolio is the combination of all three assets. The optimum portfolio P of risky assets on the PPC is found by finding the portfolio that maximizes the (ii) ratio which is equal to (iii). Graphically, it is found where the CAL is (iv) to the PPC.

27

(c) The PPC stands for the (v) and the CAL stands for the (vi). The slope of the CAL represents the additional (vii) that the investor can gain as she takes one more unit of risk.

(i)

(ii) (iii) (iv) (v)

(vi) (vii)

[8] A single-index model specifies that the excess return Ri=r i-r f of a risky asset i is determined by two risk

factors: a common factor that affects all stocks and a firm specific factor that affects only one firm. This

relationship is written as

Ri=αi+β iRm+ei

where all notations are as used in the lecture. Let μi=E (Ri), μm=E(Rm), and σ i2, σ m

2 and σ ei2 denote the

variances of Ri, Rm and e i, respectively. The index model makes the following assumptions:

(A1) E (ei|Rm )=0

(A2) (Ri ,Rm) are independently and identically distributed

These assumptions imply E (e i )=0, cov (Rm , e i )=0, and cov (e i , e j )=0 for i≠ j. Therefore, it is easy to show

E (Ri )=α i+β i μm, var (R i )=β i2σm

2 +σ ei2 , cov (Ri ,R j )=β iβ jσm

2 .

(a) Show cov (Ri ,Rm )=β iσm2 . (4 points)

cov (Ri ,Rm )=¿

(b) The risk of asset i attributable to the uncertainty common to the entire market is the term (i) and it is called the

(ii) risk, and the risk from the changes in the firm-specific factor is the term (iii) and it is called the (iv) risk. The

former is also called the (v) risk. The risk that can be removed by diversification is the (vi) risk.

(i) (β i2σm

2 , σ ei2) (ii) (systematic, non-systematic) (iii) (β i

2σm2 , σ ei

2) (iv) (systematic, non-systematic)

(v) (vi)

[9] Beta of a stock may change over time, and it is desirable to incorporate such change into the forecasting beta value.

28

(a) The estimator that takes into account the mean reversion property of betas is computed by

Adjusted beta βadj =

(b) Blume's estimator uses the common trend of betas over time and use the trend to predict the betas in

forecasting period. To do this, (i) Select two non-overlapping periods, period 1 and period 2, (ii) Estimate the beta

of each stock in each period separately. Let them be denoted by β i1 and β i2 for each stock i=1,2,,N. (iii) The

common time trend between these two sets of estimates is modeled as a linear regression model

β i2=¿

Let the estimates of intercept and slope terms be denoted by δ and γ, respectively. (iv) Forecast (estimate) the

beta in investment period (period 3) by

β i3=¿

(c) The exponentially weighted estimator of beta gives more weight on recent data than on data in distance past.

Let λ be the parameter for the exponentially weighted estimator. The OLS estimator of beta is given by

β i=∑t=1

T

(R ¿−R i)(Rmt−Rm)

∑t=1

T

(Rmt−Rm)2

The exponentially weighted estimator of beta is then written as

β i=¿

[10] The table on the next page shows information that is necessary to compute the PPC and the CAL for three

risky assets. Write proper excel commands. For (f) and (j), write the proper choice of words. (4 points each)

(a)= (b)=

(c)=

(d)=

(e) (f) (g) (h) (i) (j) (k)

29

A B C D E F G H I1 Sample means and variances-covariances of annualized monthly excess returns2 sample means and SD’s sample var and cov

IBM McD P&G IBM McD P&G14 mean i 8.19 16.17 3.63 4148.20 IBM15 SD i 64.41 54.26 51.08 1082.38 2943.86 McD16 1975.21 1311.65 2609.64 P&G

A B C D E F G H I23 Opportunity set (portfolio possibility curve PPC) Use Excel's SOLVER24 target25 p

t w1 w2 w3 p p

26 3 0.3 0.2 (a) (b) (c)27 4 0.063 0.007 0.93 4 50.242829 Optimal Portfolio30 w1 w2 w3 p p Sharpe31 (d)

Solver to find the PPC Solver to find the optimal portfolio

Set Objective: (e) Set Objective: (i)

To (f) Omax Omin Ovalue of To (j) Omax Omin Ovalue of

By changing variable cells By changing variable cells

(g) (k)

Subject to the Constrains Subject to the Constrains

(h)

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