Final Exam

intuitively the expected return on any investment should come from two components

(1) A baseline risk-free rate of return that we would demand to compensate for inflation and time value of money, even if there were no risk of losing our money. (2) A risk premium that varies with the amount of systematic risk in the investment. E= risk free rate + beta + market risk premium market risk premium = Erm - Rf

capital gains rate

(P1 - P0)/P0

dividend each year =

(earnings/shares outstanding) x dividend payout rate

bond relationships

* If price (value) of a bond is bigger than par value, the bond is premium bond. * If price (value) of a bond is less than par value, the bond is discount bond. * For premium bond, yield to maturity is smaller than coupon rate. * For discount bond, yield to maturity is bigger than coupon rate.

Arbitrage Pricing Theory (APT)

- APT does not assume that a certain level of systematic risk should result in a certain level of returns, thus a specific security price. - Rather, the relationship between systematic risk and return is a result of price adjustment for securities while "arbitrage opportunities" are always quickly erased and the prices are coming back to the level where they should be. - And it does not use market returns as a factor in the model explicitly. - APT allows multiple factors in the model.

option values

- Stock price > strike price → intrinsic value of a call option > 0 : Said to be in the money - Stock price = strike price - intrinsic value of a call option = 0 : Said to be at the money - Stock price < strike price → intrinsic value of a call option = 0 : Said to be out of the money - Stock price < strike price → intrinsic value of a put option > 0 : Said to be in the money - Stock price = strike price - intrinsic value of a put option = 0 : Said to be at the money - Stock price > strike price → intrinsic value of a put option = 0 : Said to be out of the money

types of fixed income securities

-debt obligations (bonds, mortgages, bank loans) -preferred stock

3 ways a firm can increase its divided payout rate

-increase earnings -increase dividend payout rate -decrease number of shares outstanding

what is used to discount cash flows of different types of securities?

-risk free bonds -corporate bonds -stock and dividends

CAPM Assumptions

-single factor in the model -all investors are identical, there is a universal efficient frontier -a direct relationship between risk and return (the higher the beta the more you expect to return)

two truths of diversification of a portfolio

1) By combining stocks into a portfolio, we reduce risk through diversification. 2) The amount of risk that is eliminated depends upon the degree to which the stocks move together. : Combining airline stocks reduces volatility only slightly compared to the individual stocks. : Combining airline and oil stocks reduces volatility below that of either stock.

Dow Jones Average

30 representative stocks (blue chip) used to monitor price changes on the New York Stock Exchange a price weighted index the amount invested in each company in that portfolio is proportional to the company's average share

accrued interest on T-notes and bonds

= (INT/2) x (actual number of days since last coup pmt/actual number of days in coupon period)

historical variance

= sum of squared deviations from the mean / (number of observations - 1)

unexpected return

= systematic + unsystematic

variance for a portfolio

=(weight x st dev)^2 + (weight x st dev)^2 +2(weight x st dev)(weight x st dev)(correlation coefficient)

total return

=expected return + unexpected return overtime the unexpected return component is zero

diversifiable risk

A risk that affects only some individuals, businesses, or small groups. Often considered the same as unsystematic risk

systematic risk

A risk that influences a large number of assets. Also, market risk, non diversifiable risk includes GDP, inflation, interest rates by increasing the number of securities in your portfolio you cannot reduce this type of risk

a) Johnson Motors' bonds have 10 years remaining to maturity. Coupon interest is paid annually, the bonds have a $1,000 par value, and the coupon rate is 8 percent. The bonds have a yield to maturity of 9 percent. What is the current market price of these bonds?b) BSW Corporation has a bond issue outstanding with an annual coupon rate of 7 percent paid quarterly and four years remaining until maturity. The par value of the bond is $1,000. Determine the fair present value of the bond if market conditions justify a 14 percent annual required rate of return, compounded quarterly.

A) financial calculator: N = 10, I = 9, PMT = 80, FV = 1,000,=> PV = $935.82B) financial calculator: N = 16, I = 3.5, PMT = 17.5, FV = 1,000, => PV = $788.35

constant dividend growth

Assumes that dividends will grow at a constant rate, g, forever P0 = div1 / (r-g)

The risk free rate of return is 8 percent; the expected rate of return on the market is 12 percent.Stock X has a beta coefficient of 1.3, an earnings and dividend growth rate of 7 percent, and a current dividend of $2.40. If the stock is selling for $35, what should you do?

CAPM required rate of return = r = .08 + 1.3(.12 - .08) = .132 value of stock = $2.40(1 + .07) / (.132 - .07) = $41.42 Since the stock is selling for $35, it is undervalued and should be purchased.

intrinsic value

Difference between strike price and current market value of stock. intrinsic of call = max (S-X,0) intrinsic of put = max(X-S,0)

hedging

Entering into a derivatives contract to reduce the risk associated with positions or commitments in their line of business

time and bond prices

If it is a discount bond (coupon rate < YTM), bond price increases as time goes by (approaching to maturity date). If it is a premium bond (coupon rate > YTM), bond price decreases as time goes by (approaching to maturity date). If it is a par-value bond (coupon rate = YTM), bond price does not change when approaching to maturity date. If it is a zero-coupon bond (no coupon payments), bond price increases as time goes by (approaching to maturity date).

price of a stock formula

P0=(div1 + P1)/(1 + r)

separation principle

Security transactions in a normal market neither create nor destroy value on their own. Therefore, we can evaluate the NPV of an investment decision separately from the decision the firm makes regarding how to finance the investment or any other security transactions the firm is considering.

treasury STRIPS

Separate Trading of Registered Interest and Principal of Securities. A zero-coupon bond issued by the U.S. Treasury in which all interest income is received at maturity in the form of a higher (accreted) principal value. Avoids "reinvestment risk"

A bond matures in 2020 and has an annual coupon of 3.65 percent, payable on January 1 and July 1. The current price of the $1,000 bond is $978. On January 30, you purchase $10,000 face amount (settlement date is February 2), and your broker charges a $25 commission. How much must you remit for the purchase?

Since the bond pays $365 a year ($10,000 x 0.0365), the accrued interest owed is $32 (32 days × $365/365). The total that has to be remitted is :$9,780 + 25 + 32 = $9,837.

risk premiums

The "extra" return earned for taking on risk Treasury bills are considered to be risk-free The risk premium is the return over and above the risk-free rate thus for any investment at the market return=risk free rate+risk premium

buying a put option

The buyer of a put option on a stock has the right (but not the obligation) to sell the underlying stock to the writer of the option at an agreed upon exercise price (X, e.g., $9.00). In return for this option, the buyer of the put option pays a premium (P, e.g., $0.65) to the option writer. - The lower the price of the underlying stock at the expiration of the option, the higher the profit to the put option buyer upon exercise. - As the underlying stock's price rises, the probability that the buyer of a put option has a negative payoff increases. → Thus, buying a put option is an appropriate position when the price on the underlying asset is expected to fall.

time value of an option

The difference between an option's price (or premium) and its intrinsic value. Time value of an option is a function of 1) The price volatility of the underlying asset 2) The time until the option matures (its expiration date)

capital market line

The tangent line drawn from the point of the risk-free asset to the feasible region for risky assets

selling a put option

The writer or seller of a put option receives a fee or premium (P, e.g., $0.65) in return for standing ready to buy the underlying stock at the exercise price (X, e.g., $9.00) should the buyer of the put choose to exercise the option. - When the underlying stock's price rises, the put option writer has an enhanced probability of making a profit. - When the underlying stock's price falls, the writer of the put option is exposed to potentially large losses. → Thus, writing a put option is an appropriate position if the price on the underlying asset is expected to rise

yield to maturity

The yield earned on a bond from the time it is acquired until the maturity date

biggest shortfall of CAPM

Unrealistic nature of the assumptions → Assumption #1: CAPM assumes that the market's return is the only factor that can explain the variation in individual stock's returns. IMPROVEMENT: multiple factors Assumption #2: CAPM assumes that "all investors are identical in every way but wealth and risk aversion." IMPROVEMENT: dont use efficient frontier Assumption #3: CAPM assumes a direct relationship between risk and return. An investor should be willing to take a certain level of risk to get returns. (i.e. the higher the beta, the more you expect to earn.) IMPROVEMENT: no use of market returns

registered bond

a bond in which the owner is recorded by the issuer and the coupon payments are mailed to the registered owner

derivative

a contract between two parties whose value is based on some underlying asset price or condition two parties exchange a standard quentity of an asset at a predetermined price at a specific date in the future types include future, forwards, option, swaps

dividend discount model

a model that values shares of a firm according to the present value of the future dividends the firm will pay

best efforts underwriting

a public offering in which the investment bank does not guarantee a firm price

firm commitment underwriting

a public offering of Munis made through an investment bank, where the investment bank guarantees a price for the newly issued bonds by buying the entire issue and then reselling it to the public

unsystematic risk

a risk that affects at most a small number of assets. Also, unique or asset-specific risk includes labor strikes, part shortages, etc. you can diversify this type of risk away

realized returns....

are generally not equal to expected returns

geometric average

average compound return per period over multiple periods, less than the arithmetic average unless all the returns are equal overly pessimistic for short term, so if 40+ years, use geo

What must be the price of a $10,000 bond with a 5% coupon rate, semiannual coupons, and two years to maturity if it has a yield to maturity of 5% APR? a. $10,619.63 b. $10,000.00 c. $10,940.49 d. $9,113.51

b. $10,000.00

If an investor were to anticipate that interest rates were going to fall, that investor should; a. take no action b. buy bonds c. sell bonds d. acquire money market securities

b. buy bonds

The accrued interest on a bond a. avoids personal income taxation b. is paid by the buyer of the bond to the seller of the bond c. is the result of the possibility of the bond defaulting d. applies only to zero coupon bonds

b. is paid by the buyer of the bond to the seller of the bond

A put is an option to a. receive stock b. sell stock c. buy stock d. receive dividends

b. sell stock

discount bond

bond price < bond face (par) value → Coupon rate < Yield to maturity

par value bond

bond price = bond face (par) value → Coupon rate = Yield to maturity

premium bond

bond price > bond face (par) value → Coupon rate > Yield to maturity

private placement

bonds are sold on a semi-private basis to qualified investors (generally FIs)

bearer bond

bonds with coupons attatched to the bond

speculation

buying and selling risky items in the hope of making a quick profit

The Standard & Poor's 500 stock index illustrates a. a geometric index b. an exponential index c. a value-weighted index d. a simple average

c. a value-weighted index

A call is an option to a. sell stock at a specified price b. deliver bonds at a specified price c. buy stock at a specified price d. deliver stock at a specified price

c. buy stock at a specified price

The yield to maturity on a bond is a. below the coupon rate when the bond sells at a discount and equal to the coupon rate when the bond sells at a premium. b. None of the options c. the discount rate that will set the present value of the payments equal to the bond price. d. based on the assumption that any payments received are reinvested at the coupon rate.

c. the discount rate that will set the present value of the payments equal to the bond price.

The accrued interest on a bond a. is the result of the possibility of the bond defaulting b.applies only to zero coupon bonds c.is paid by the buyer of the bond to the seller of the bond d.avoids personal income taxation

c.is paid by the buyer of the bond to the seller of the bond

american option

can be exercised on or before its expiration

european option

can be exercised only on the expiration date

Par Value Bond Discount bond Premium bond

coupon rate = YTM coupon rate < YTM coupon rate > YTM

arbitrage

creation of riskless profits made possible by relative mispricing among securities

two components of returns

current income and capital gains or losses

While bond prices fluctuate, a. yields are constant b. short term bond prices fluctuate more c. the spread between yields is constant d. coupons are constant

d. coupons are constant

Ceteris paribus, the price and yield on a bond are a.indefinitely related. b.not related. c.positively related. d.sometimes positively and sometimes negatively related. e. negatively related.

e. negatively related.

Chicago Board Options Exchange (CBOE)

first exchange devoted to trading of stock options

put provision of bond

gives the bondholder the right to sell the issue back to the issuer at par value on designated dates

call provisions of bonds

grants the issuer the right to retire the debt either fully or partially before the scheduled maturity date

efficient frontier

graphical representation of a set of possible portfolios that (1) minimizes risk at a specific return levels and (2) maximizes returns at specific risk levels, located on the opportunity set above MVP

if an investor is risk averse...

he will find a point closer to the risk free interest rate *note that all investors have the same CML

zero coupon bond

interest is paid at the maturity with the exact amount being the difference between the principal value and the price paid for the bond two cash flows: 1. market price at the time of purchase 2. bonds face value at maturity always trade for a discount

put option

is an option that gives the purchaser the right, but not the obligation, to sell the underlying security to the writer of the option at a specified exercise price on (or up to) a specified date.

treasury notes and bonds

issued by the U.S. government to finance expenditures; no default risk but prices change when market rates change

floating rate bonds

issues where the coupon rate resets periodically (the coupon reset date) based on the coupon reset formula given by: reference rate + quoted margin

bond indenture

legal document containing complete details of a bond issue

covered option writing

less risky The investor buys (or already owns) the underlying stock and then sells the option to buy that stock. If the option is exercised, the investor supplies the stock that was previously purchased (i.e., covers the option with the stock).

corporate bonds

long-term debt issued by private corporations typically paying semiannual coupons and returning the face value of the bond at maturity

naked writing option

more risky Selling the call without owning the stock. The investor is exposed to considerable risk. If the price of the stock rises and the call is exercised, the option writer must buy the stock at the higher market price in order to supply it to the buyer. With naked option writing, the potential for loss is considerably greater than with covered writing

to cover the position...

option sellers can buy their own issues. : As the option contracts get closer to their expiration date, open interest (existing number of contracts) decreases, since the sellers keep on buying back the options they issued.

interest

payment for the use of money

security characteristics line

plot of a security's predicted excess return from the excess return of the market r= alpha + beta + e if beta is bigger, the systematic risk is higher

value of a firm =

price of a share x number of outstanding shares

put/call ratio

ratio of put options to call options outstanding on a stock open interest of put options for a security divided by open interest of call options for the same security. •When investors are bullish on the underlying security: the ratio goes down. •When investors are bearish on the security: the ratio goes up. When the ratio > 1, investors are pessimistic about the security

arithmetic average

return earned in an average period over multiple periods overly optimistic for long term, so if 15-20 years or less use this one

abnormal return

return that exceeds what is justified by the risk associated with the investment = actual return - market return on that same day

optimal portfolio of risky securities

tangent point between CML and efficient frontier

term vs serial bond

term: a single maturity date for one series serial: a multiple maturity dates for one series, hedging the risk for maturity crisis

beta coefficient

the amount of systematic risk present in a particular risky asset relative to that in an average risky asset higher beta-higher sensitivity to the market-higher systematic risk beta of a portfolio = (weight of sec x beta of sec 1) + (weight of sec 2 x beta of sec 2)

principal

the amount owed, the face value of a debt

correlation

the covariance divided by the product of standard deviations of two funds ranges from -1 to 1 if correlation is 1, it means that the stock move together perfectly and the effect of diversification becomes 0

yield to maturity of a zero coupon bond

the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond = [(face value/price)^(1/n)] -1

dividend yield

the dividend per share divided by the stock price

the greater the volatility...

the greater the uncertainty

minimum variance portfolio

the portfolio of risky assets with lowest variance

yield curve

the relationship between time to maturity and yields for debt in a given curve

required return

the return necessary to induce the investor to purchase an asset when considering (1) opportunity cost from alternative options and (2) risk associated with the asset

coupon payment

the specified periodic payments proportional to the principle amount

realized return

the sum of income and capital gains earned on an investment

expected return

the sum of the anticipated dividend yield and capital gains =sigma(probability times return)

dollar returns

the sum of the current income received plus the change in the value of the asset in dollars

percentage returns

the sum of the current income received plus the change in value of the asset divided by the initial investment

maturity date

the time at which a debt issue becomes due and the principal must be repaid

price/earnings ratio method

the value of a stock is the product of the earnings per share and the benchmark P/E ratio P=(P/E)E

total assets of a firm =

total debt + total equity

event study

used to prove semi-strong from market efficiency, it examines prices and returns over time

returns for a portfolio

weighted average of the expected returns on the securities of the portfolio =weight x expected return

duration (macaulay duration)

weighted average time to maturity using present values of the cash flows as weights 1) Longer term to maturity means a higher sensitivity of bond price to the interest rate changes (higher interest rate risk). 2) Lower coupon rate means a higher sensitivity of bond price to the interest rate change (higher interest rate risk).

call option

an option that gives the purchaser the right, but not the obligation, to buy the underlying security from the writer of the option at a specified exercise price on (or up to) a specified date. buying a call option is appropriate option when the underlying assets price is expected to rise writing a call option is appropriate option when the underlying assets price is expected to rise

shortfalls of constant dividend growth model

1. valuation of firms not paying dividends 2. assumptions used in the model (return on investment, erratic future dividends, etc.)

municipal bonds

Bonds issued by state and local governments typically in minimum denominations of $5,000 to finance imbalances or long term capital outlays attractive to household investors because interest is exempt from federal and most local income taxes two types include general obligation and revenue bonds

The price of a stock is $51. You can buy a six-month call at $50 for $5 or a six-month put at $50 for $2. a) What is the intrinsic value of the call? b) What is the intrinsic value of the put? c) What is the time premium paid for the call? d) What is the time premium paid for the put? e) If the price of the stock falls, what happens to the value of the put? f) What is the maximum you could lose by selling the call covered? g) What is the maximum possible profit if you sell the stock short?* Questions h - k assume the passage of six months. After six months, the price of the stock is $58. h) What is the value of the call? i) What is the profit or loss from buying the put? j) If you had sold the stock short six months earlier, what would your profit or loss be? k) If you had sold the call covered, what would your profit or loss be?

a) $51 - 50 = 1$ b) $50 - 51 = -1 -> cant be negative -> = $0 c) $5 - 1 = $4 d) $2 - 0 = $2 e) Stock price and value of put options are inversely related, so the value of the put would rise f) f. If the investor sells the call covered, the maximum possible loss is the cost of the stock minus the proceeds of the sale of the call: $51 ‑ 5 = $46. g) If the price of the stock fell to $0, the profit (and the maximum possible profit) on the short position is $51. h) The intrinsic value (price) of the call is $58 - 50 = $8. i) The put is worthless; loss is the purchase price: $2 j) The loss would be $51 ‑ 58 = ($7). k) . Profit on the stock: $58 ‑ 51 = $7Loss of the option: $5 ‑ 8 = (3)Net profit: $4

Calculate the yield to maturity on the following bonds.a) A 9 percent coupon (paid semiannually) bond, with a $1,000 face value and 15 years remaining to maturity. The bond is selling at $985.b) An 11 percent coupon (paid annually) bond, with a $1,000 face value and 6 years remaining to maturity. The bond is selling at $1,065.

a) financial calculator: N = 30, PV= -985, PMT = 45, FV = 1,000, => I = ytm = 4.593% for 6 months or 9.186% per year.B) financial calculator: N = 6, PV= -1,065, PMT = 110, FV = 1,000, => I = ytm = 9.528%

Which of the following statements is correct? a. If a bond sells for a discount, the yield to maturity exceeds the coupon interest rate. b. As interest rates increase, the prices of existing bonds increase. c. The prices of twenty year bonds tend to fluctuate less than bonds with five years to maturity. d. The smaller the duration, the more volatile the bond's price.

a. If a bond sells for a discount, the yield to maturity exceeds the coupon interest rate.

Preferred stock and long term bonds are similar because a. interest and dividend payments are fixed b. they both have voting power c. interest and dividend payments are legal obligations d. interest and dividend payments are tax deductible expenses

a. interest and dividend payments are fixed

The time premium paid for an option to buy stock is affected by a. the length of time to expiration b. the existence of a rights offering c. the firm's financial statements d. the firm's credit rating

a. the length of time to expiration

The intrinsic value of an option to buy stock rises as a. the strike price decreases and the price of the stock rises b. the strike price increases and the price of the stock declines c. the strike price decreases and the price of the stock declines d. the strike price increases and the price of the stock rises

a. the strike price decreases and the price of the stock rises

opportunity set

all possible combinations of consumption that someone can afford given the prices of goods and the individual's income