FIN 353 CHs 9-13 EXAM

prime rate

The basic interest rate on short-term loans that the largest commercial banks charge to their
most creditworthy corporate customers

federal funds rate

Interest rate that banks charge each other for overnight loans of $1 million or more.

discount rate

The interest rate that the Fed offers to commercial banks for overnight reserve loans

banker’s acceptance

A postdated check on which a bank has guaranteed payment. Commonly used to
finance international trade transactions

call money rate

The interest rate brokerage firms pay for call money loans from banks. This rate is used
as the basis for customer rates on margin loans.

commercial paper

Short-term, unsecured debt issued by the largest corporations

CDs

The interest rate on certificates of deposit, which are large-denomination deposits of $100,000 or
more at commercial banks.

London Interbank Offered Rate (LIBOR)

• Interest rate that international banks charge one
  another for overnight Eurodollar loans.

• being replaced in the US by the Secured Overnight Financing Rate (SOFR)

• SOFR is the rate on repurchased Treasury securities and is published daily by the New York Federal Reserve

Eurodollars

U.S. dollar denominated deposits in banks outside the United States

Euro LIBOR

refers to deposits denominated in euros—the common currency of 19 European
Union countries.

EURIBOR

is an interest rate that also refers to deposits denominated in euros. However, EURIBOR
is based largely on interest rates from the interbank market for banks in the European Union

HIBOR

is an interest rate based on Hong Kong dollars; interest rate among banks in
the Hong Kong interbank market.

US treasury bill (T-bill)

a short term US government debt instrument issued by the US Treasury

pure discount security

• is an interest bearing asset

• makes a single payment of face value at maturity

• makes no payments before maturity

• bank discount basis

• bond equivalent yields (BEY)

• annual percentage rates (APR)

• effective annual rates (EAR)

different ways market participants quote interest rates

bank discount basis

• is a method of quoting interest
  rates on money market instruments, such as T-bills and banker’s acceptances

• formula: Current price= face value x [1-(days to maturity/360) x discount yield]

• the term discount yield simply refers to the quoted interest rate

bond equivalent yield (BEY)

• another way to quote an interest rate

• converting a bank discount yield to this: BEY= [(365 x discount yield) / (360 - days to maturity x discount yield)]

“simple” interest basis

• another method to quote interest rates

• calculated just like annual percentage rates

• used for CDs

• bond equivalent yield on a T-bill with less than six months to maturity is also an APR

annual percentage rates (APR)

understates the true interest rate, which is usually called the effective annual rate (EAR)

1+EAR= [1+(APR/m)]^m

formula for converting APRs to EARs

rates and yields on fixed income securities

• Fixed-income securities include long-term debt contracts from a wide variety of issuers: US government, real estate purchases (mortgage debt), corporations, municipal governments

• When issued, fixed-income securities have a maturity of greater than one year

• When issued, money market securities have a maturity of less than one year.

  
  

treasury yield curve

• is a plot of Treasury yields against
  maturities.

• It is fundamental to bond market analysis, because it represents the interest rates for default-free lending across the maturity spectrum.

  
  

term structure of interest rates

• is the relationship between time to maturity and the interest rates for default- free, pure discount instruments

• is sometimes called the “zero-coupon yield
  curve” to distinguish it from the Treasury yield curve, which is based on coupon bonds.

• can be seen by examining yields on US treasury STRIPS

  
  

STRIPS

• are pure discount instruments created by “stripping” the coupons and principal payments of U.S. Treasury notes and bonds into separate parts, which are then sold separately

• stands for Separate Trading of Registered
  Interest and Principal of Securities

• Price= [face value / (1+ (YTM/2))²M]

Nominal interest rates

are interest rates as they are observed and quoted, with no adjustment for inflation

real interest rates

• = nominal interest rate - inflation rate

• interest rates that are adjusted for inflation effects

Fisher Hypothesis

• asserts that the general level of nominal interest rates follows the general level of inflation

• according to this, interest rates are, on average, higher than the rate of inflation

inflation- indexed treasury securities

• adjust their principal semiannually according to the most recent inflation rate

• pay a fixed coupon rate on their current principal.

expectations theory

• The term structure of interest rates reflects financial market beliefs about future interest rates.

• The term structure is almost always upward sloping, but interest rates have not always risen

• it is often the case that the term structure turns down at very long maturities

market segmentation theory

• Debt markets are segmented by maturity, so interest rates for various maturities are determined separately in each segment

• The U.S. government borrows at all maturities

• Many institutional investors, such as mutual funds, are more than willing to move maturities to obtain more favorable rates

• There are bond trading operations that exist just to exploit perceived premiums, even very small ones

maturity preference theory

• Long-term interest rates contain a maturity premium necessary to induce lenders into making longer term loans

• The U.S. government borrows much more heavily short-term than long- term.

• Many of the biggest buyers of fixed-income securities, such as pension funds, have a strong preference for long maturities.

  
  

forward rate

• is an expected rate on a short-term security
  that is to be originated at some point in the future

• one year forward rate= (1+r2)²= (1+r1) (1+f1,1)

interest rate risk

Long-term bond prices are much more sensitive to
interest rate changes than short-term bonds

straight bond

• is a IOU that obligates the issuer of the bond to pay the holder of the bond: a fixed sum of money (called the principal, par value, or face value) at the bond’s maturity; constant periodic interest payments (called coupons) during the life of the bond

US treasury bonds

straight bonds that may have special features attached such as convertible bonds, callable bonds, and putable bonds

coupon rate

= annual coupon/par value

current yield

= annual coupon/bond price

by adding together the present value of the bond’s coupon payments and the present value of the bond’s face value

how is the price of a bond found?

yield to maturity

is the discount rate that equates today’s bond price with the present value of all the future cash flows of the bond

premium bonds

• if coupon rate > YTM then price > face (par value)

• the longer the term to maturity, the greater the premium over par value

• coupon rate > current yield > YTM

discount bonds

• if coupon rate < YTM then price < face (par value)

• the longer the term to maturity, the greater the discount from par value

• coupon rate < current yield < YTM

par bonds

• if coupon rate = YTM then price = face (par value)

• coupon rate = current yield = YTM

clean or flat price

quoted price net of accrued interest

dirty price

the price the buyer actually pays

callable bond

gives the issuer the option to buy back the bond at a specified call price anytime after an initial call protection period

yield to call

is a yield measure that assumes a bond will be called at its earliest possible call date

interest rate risk

the possibility that changes in interest rates will result in losses in the bond’s value

realized yield

the yield actually realized on a bond

malkiel’s theorems

1. bond prices and bond yields move in opposite directions

   1. as a bond’s yield increases, its price decreases

   2. conversely, as a bond’s yield decreases, its price increases

2. for a given change in bonds YTM, the longer the term to maturity of the bond, the greater the magnitude of the change in the bond’s price

3. for a given change in a bond’s YTM, the size of the change in the bond’s price increases at a diminishing rate as the bond’s term to maturity lengthens

4. for a given change in a bond’s YTM, the resulting percentage change in the bond’s price is inversely related to the bonds coupon rate

5. for a given absolute change in a bonds YTM, the magnitude of the price increase caused by a decrease in yield is greater than the price decrease caused by an increase in yield

Macaulay duration, or duration

• a way for bondholders to measure the sensitivity of a bond price to changes in bond yields

• two bonds with the same of this, but not necessarily the same maturity, will have approximately the same price sensitivity to a small change in bond yields

• values are stated in years and are often described as a bond’s effective maturity

zero coupon bond

duration = maturity

coupon bond

duration = a weighted average of individual maturities of all the bonds separate cash flows, where the weights are proportionate to the present values of each cash flow

duration properties

• all else the same, the longer a bond’s maturity, the longer its duration

• all else the same, a bond’s duration increases at a decreasing rate as maturity lengthens

• all else the same, the higher a bond’s coupon, the shorter is its duration

• all else the same, a higher yield to maturity implies a shorter duration

dollar value of an 01

measures the change in bond price from a one basis point change in yield

yield value of a 32nd

measures the change in yield that would lead to a 1/32nd change in the bond price

dedicated portfolios

a bond portfolio created to prepare for a future cash payment; day payment is due is commonly called the portfolio’s target date

reinvestment rate risk

• the uncertainty about the value of the portfolio on the target date

• reinvestment rate risk stems from the need to reinvest bond coupons at yields not known in advance

price risk

• risk that bond prices will decrease

• arises in dedicated portfolios when the target date value of a bond is not known with certainty

immunization

the term for constructing a dedicated portfolio such that the uncertainty surrounding the target date value is minimized

duration matching

matching the duration of the portfolio to its target date

dynamic immunization

• a periodic rebalancing of a dedicated bond portfolio for the purpose of maintaining a duration that matches the target maturity date

• advantage: reinvestment risk caused by continually changing bond yields is greatly reduced

• drawback: each rebalancing incurs management and transaction costs

expected return

• the weighted average return on a risky asset from today to some future date

• = sum of [ps x returni,s]

expected risk premium

= expected return - riskfree rate

variance of expected returns

= sum of [ps x (returns - expected return)²]

portfolios

• groups of assets, such as stocks and bonds, that are held by an investor

• a way to describe it is by listing the proportion of the total value of the portfolio that is invested into each asset

• these proportions are called portfolio weights which are sometimes expressed in percentages

expected return on a portfolio

• linear combination, or weighted average, of the expected returns on the assets in that portfolio

• = sum of [wi x E(Ri)]

portfolio variance

• = sum of [ps x {E(Rp,s) - E(Rp)}²]

fallacy of time diversification

• typical argument: even though stocks are more volatile, over time, the volatility cancels out

• this is incorrect

• although the standard deviation of average geometric return tends to zero as the time horizon grows, the standard deviation of your wealth does not tend to zero

• wealth volatility increases over time; it does not cancel out over time

• investing in equity has a greater chance of having an extremely large value and increases the probability of ending with a very low value

correlation

• the tendency of the returns on two assets to move together; imperfect is the key reason why diversification reduces portfolio risk as measured by the portfolio standard deviation

• positively: assets tend to move up and down together

• negatively: assets tend to move in opposite directions

correlation coefficient

• denoted by Corr(Ra, Rb)

• measures correlation and ranges from -1 to 1

  • - 1 (perfect negative correlation)

  • 0 (uncorrelated)

  • 1 (perfect positive correlation)

investment opportunity set

curve that shows the possible combinations of risk and return available from portfolios of two assets

efficient portfolio

portfolio that offers the highest return for its level of risk

dominated or inefficient portfolios

undesirable portfolios

markowitz efficient frontier

• the set of portfolios with the maximum return for a given risk and the minimum risk given a return

• on the plot, the upper left hand boundary on the plot is this

• all other possible combinations are inefficient; investors would not hold these portfolios because they could get either more return for a given level of risk or less risk for a given level of return

normal return

• expected part of the return is the return that investors predict or expect

• total return = expected return + unexpected return

uncertain return

• risk part of the return comes from unexpected information revealed during the year

• = total return - expected return

announcements and news

• firms makes periodic announcements about events that may significantly impact the profits of the firm (earnings, new products, personnel)

• impact of the announcement depends on how much of the announcement represents new information

  • when the situation is not as bad as previously thought, what seems to be bad news is actually good news

  • when the situation is not as good as previously thought, what seems to be good news is actually bad news

• market participants put predictions into the expected part of the stock return

• announcement = expected news + surprise news

systematic risk

• the risk that influences a large number of assets; also called market risk

• also called non-diversifiable risk

unsystematic risk

• risk that influences a single company or small group of companies; also called unique risk or firm-specific risk

• also called diversifiable risk

total risk

= systematic risk + unsystematic risk

systematic risk principle

• states the expected return on an asset depends only on its systematic risk

• no matter how much total risk an asset has, only the systematic portion is relevant in determining the expected return (and risk premium) on that asset

beta coefficient

• measures the relative systematic risk of an asset

• assets with this larger than 1 has more systematic risk than average

• assets with this smaller than 1 have less systematic risk tha average

• asstes with larger of this have will have greater expected returns

security market line (SML)

a graphical representation of the linear relationship between systematic risk and expected return in financial markets

capital asset pricing model (CAPM)

theory of risk and return for securities in a competitive capital market

performance evaluation

a term for assessing how well a money manager achieves a balance between high returns and acceptable risks

raw return on a portfolio

• simply the total percentage on a portfolio

• a naive performance evaluation because it has no adjustment for risk and is not compared to any benchmark, or standard

• usefulness on a portfolio is limited

Sharpe ratio

• reward to risk ratio that focuses on total risk

• it is computed as a portfolio’s risk premium divided by the standard deviation of the portfolio’s return

Sortino Ratio

• another reward to risk ratio that focuses on downside risk

• designed to penalize investment managers for having undesirable risk

• computed like the Sharpe ratio but the standard deviation uses only returns that lie below the mean

treynor ratio

• reward to risk ratio that looks at systematic risk only

• computed as a portfolio’s risk premium divided by the portfolio’s beta coefficient

jensen’s alpha

• the excess return above or below the security market line; can be interpreted as a measure of by how much the portfolio “beat the market”

• computed as the raw portfolio return less the expected portfolio return as predicted by the CAPM

• One way: Evaluate the significance level of the alpha estimate using a regression.

• Another way: Calculate the fund’s information ratio

How do we know whether a mutual fund’s alpha is statistically significantly different
from zero or simply represents a result of random chance?

information ratio

• a fund’s alpha divided by its tracking error

• higher one means a lower tracking error risk

tracking error

measures the volatility of the funds returns relative to its benchmark

r squared

• simply the squared correlation of the fund to the market, R

• represents the percentage of the fund’s movement that can be explained by movements in the market

• An R-squared of 100 indicates that all movements in the security are driven by the market, indicating a correlation of −1 or +1

• A high R-squared value (say, greater than .80) might suggest that the performance measures (such as alpha) are more representative of potential longer-term performance

global investment performance standards (GIPS)

Goal: Provide a consistent method to report portfolio performance to prospective (and current) clients

investment risk management

concerns a money manager’s control over investment risks, usually with respect to potential short-run losses.

value at risk (VaR)

• is a technique of assessing risk by
  stating the probability of a loss that a portfolio may experience within a fixed time horizon.

• If the returns on an investment follow a normal
  distribution, we can state the probability that a portfolio’s return will be within a certain range, if we have the mean and standard deviation of the portfolio’s return.

• price= [face value / {1+ (YTM/2)}²(years)

  • = [100 / {1+(.035/2)}^10×2= $70.68

What is the price of a Treasury STRIPS with a face value of $100 that matures in 10 years and has a yield to maturity of 3.5 percent?

• YTM= 2 x [(100/quoted price)^(1/2xyears) - 1]

  • = 2 x [(100/90.875)^(1/(2×5) - 1]= 1.92%

A Treasury STRIPS is quoted at 90.875 and has 5 years until maturity. What is the yield to maturity?

• real return= percent last year - inflation rate

  • = 8.9%-2.1%= 6.8%

A stock had a return of 8.9 percent last year. If the inflation rate was 2.1 percent, what was the approximate real return?