FINAN 3050 FINAL EXAM Review

Ch 12 Q5 You own a stock portfolio invested 10 percent in stock Q, 25 percent in stock R, 50 percent in stock S, and 15 percent in stock T. The betas for these four stocks are 1.4, 0.6, 1.5, and 0.9, respectively. What is the portfolio beta?

(0.1*1.4) + (0.25*0.6) + (0.5*1.5) + (0.15*0.9) = 1.175

Ch 12 Q9 A share of stock sells for $35 today. The beta of the stock is 1.2 and the expected return on the market is 12 percent. The stock is expected to pay a dividend of $0.80 in one year. If the risk-free rate is 5.5 percent, what should the share price be in one year?

0.055 + 1.2*(0.12-0.055) = 13.3% = Er [(P1 + 0.8) - 35]/35 = 0.133 0.133*35 = P1 - 34.2 4.655 + 34.2 = P1 = 38.86

Ch 12 Q2 A stock has an expected return of 8.0 percent, its beta is 0.60, and the risk-free rate is 3 percent. What must the expected return on the market be?

0.08 = 0.03 + 0.6*MRP 0.08 -0.03 / 0.6 = 0.08333 = MRP = Expected return on market - 0.03 Expected return on market = 0.08333 + 0.03 = 11.33%

Ch 12 Q4 A stock has a beta of 0.8 and an expected return of 11 percent. If the risk-free rate is 4.5 percent, what is the market risk premium?

0.11 = 0.045 + 0.8*MRP 0.11 - 0.045/0.8 = 8.125% = MRP

Ch 12 Q3 A stock has an expected return of 12 percent and a beta of 1.4, and the expected return on the market is 10 percent. What must the risk-free rate be?

0.12 = Rf + 1.4*(0.1-rf) 0.12 = Rf + 0.14 - 1.4rf 0.12 - 0.14 = Rf -1.4Rf -0.02 = -0.4Rf 5% = Rf

Ch 12 Q1 A stock has an expected return of 13.2 percent, the risk-free rate is 3.5 percent, and the market risk premium is 7.5 percent. What must the beta of this stock be?

0.132 = 0.035 + B*0.075 0.132 - 0.035/0.075 = B = 1.29

Ch 12 Q7 You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.20 and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio?

1 = 0.33*1.2 + 0.33X + 0.33*0 1 - (0.33*1.2) = 0.33X 0.6 = 0.33X X = 1.8

Ch 12 Q6 You own 400 shares of stock A at a price of $60 per share, 500 shares of stock B at $85 per share, and 900 shares of stock C at $25 per share. The betas for the stocks are 0.8, 1.2, and 0.7, respectively. What is the beta of your portfolio?

A = 400*60 = 24,000/89,000 = 0.26966 B = 500*85 = 42,500/89,000 = 0.47753 C = 900*25 = 22,500/89,000 = 0.25281 total: 24,000 + 42,500 + 22,500 = 89,000 (0.26966*0.8) + (0.47753*1.2) + (0.25281*0.7) = 0.96573 = 0.97

Chapter 12 What is a high beta?

A high beta is a beta over 1. This means the beta is higher than the market beta, which is 1. It is riskier and deserves a higher return.

Chapter 12 What is a low beta?

A low beta is a beta under 1. It is lower than the market beta which is 1. Between 0-1 It is less risky and deserves less return than the market.

Ch. 10 Know how to calculate: Current yield

Annual coupon/Price of bond

Ch 10 What does it mean when bonds have superior claims in hierarchy?

Any payment the firm makes to any owners or claimants must be paid to bondholders before equity holders

Ch 12 Example: how to use the beta of a portfolio to achieve a target based on the beta of a portfolio from the weighted average of the betas of the individual assets. Rf = 0.01 MRP = 0.068 Risk free beta = 0 Stock X Beta = 1.8 Target portfolio E(rp) = 0.1 What should the beta of the portfolio be if the expected return on the portfolio is 10%? What is the risk-free weighted average? What is the expected return on stock x? What is the expected return on the portfolio?

Beta of portfolio: E(rp) = 0.02 + Bp*0.068 = 0.10 (0.10 - 0.02)/0.068 = 1.3235 Risk-free weighted average: Bp = Wx(Bx) + Wrf(Brf) Wrf = 1 - Wx Wx*1.8 + (1-Wx)*0 = 1.3235 Wx = 1.3235/1.8 = 0.7353 = Wx Wrf = 1 - 0.7353 = 0.2647 Expected return on stock x: E(rX) = 0.01 + 1.8*0.068 = 0.1324 = 13.24% Expected return on the portfolio: E(rP) = 13.24%*0.7353 + 1%*0.2647 = 0.1

Chapter 12 What is the CAPM?

CAPM is the capital asset pricing model. It is used to calculate fair rate of return vs. risk. It is used for valuation, return used for valuation, and time value discounting.

Ch 10 What are special feature bonds?

Convertibles, consols, deferred coupons, puttables

Ch. 10 What is current yield?

Coupon as % of price does not consider price appreciation/depreciation. The coupon divided by the bond's price (the PV). Quick way of seeing the kind of return you're getting based on what you paid for it. Fails to take into account appreciation/depreciation of the bond throughout time.

Ch 10 What is the maturity date?

Date when the par value is paid.

Chapter 12 Why is beta the only measure of risk that is rewarded in the competitive market (why is diversifiable risk notrewarded)?

Diversifiable risk is not rewarded in the competitive market because it doesn't cost money to get rid of risk. Beta shows systematic risk, and diversifiable risk. Non diversifiable risk can't be eliminated as easily as diversifiable risk. Higher risk should be rewarded

Chapter 12 What is the difference between diversifiable and non-diversifiable risk?

Diversifiable risk represents non-systematic risk. This type of risk can be reduced by diversification. We eliminate this risk by building portfolios. It is not rewarded in the market because it can easily be eliminated without any costs. Non-diversifiable risk is also market/systematic risk. This risk is rewarded in the market. This is the risk that is still present even when there's no diversifiable risk.

Chapter 12 What other names are used for diversifiable and non-diversifiable risk?

Diversifiable risk: unique, asset specific, non-systematic, idiosyncratic risk Non-diversifiable: market, beta, systematic risk.

Ch. 10 What is duration?

Duration is a tool that managers use to assess how much interest rate risk there is in their portfolio. Duration is the weighted average of the times until various payments are made Duration is an average maturity. The higher the duration of the portfolio, the more exposure you have to changes in market interest rates

Ch 12 E(p1) = $44 E(D1) = $2.08 B = 1.12 rf = 1.6% MRP = 7.1% P0(actual) = $43 P0(fair) = ? E(r)(fair) = ? E(r)(actual) = ? Over/under priced?

E(r)(fair) = 0.016 + 1.12*0.071 = 0.09552 = 9.552% P0(fair) = [E(P1) + E(D1)]/(1+k) (44+2.08)/(1.09552) = 42.06 E(r)(actual) = (E(P1) + E(D1) - P0)/P0 (44 +2.08 -43)/43 = 0.07163 = 7.16% 7.16% actual < 9.55% fair, don't buy, return is too low 43 actual > 42.06 fair overpriced, should not invest Price is too high, return is too low

Chapter 12 example Asset = Q Expected price E(p1,Q) = $100 Expected dividend E(D1,Q) = $2 Beta of Q Bq = 1.42 Risk-free rate rf = 2% Expected return on the market E(rm) = 9.2% P0(actual) the actual price = $88 What is the fair rate of return? E(rQ)(fair) =? What is the fair price? P0(fair) = ? Is the stock over or under priced? Should you buy it? What is the actual return? E(rQ) = ? Or holding period return (HPR)? What is the alpha? By how much is the actual return greater than the fair rate of return?

E(rQ)(fair) = 2% + 1.42*(9.2%-2%) = 12.224% P0(fair) = (100+2)/(1+12.224%) = $90.89 $90.89 - 88 = 2.89 Overpriced, so buy it E(rQ)(actual) or HPR = [(100+2)-88]/88 = 15.909% 15.909% - 12.224% = 3.685% = alpha 3.685% greater than the fair rate of return

Ch 12 rf = 4% MRP = 6.5% Target E(rp) = 9.6% Bp = ? Is this asset more or less risky than the market?

E(rp) = rf +Bp(E(rm) - rf) 0.04 + Bp (0.065) = 0.096 (0.096 - 0.04)/0.065 = 0.862 = Bp 1 > 0.862, this asset is less risky than the market

Ch 12: Fair vs. Actual pricing Bx = 1.63 rf = 1.8% E(rm) = 9% E(P1) = $79.14 E(rx)(Fair) = ? Px0(fair) = ? Suppose that Px0(actual) = $68, is the asset under or over-priced? Is this a good investment? E(rx)(actual) = ? What is the excess return?

E(rx)(fair) = 0.018 + 1.63*(0.09-0.018) = 0.13536 = 13.54% Px0(fair) = FV/(1+k) = 79.14/(1.1354) = $69.70 $69.70 > $68 under priced Should invest E(rx)(actual) = (FV - P0)/P0 = (79.14 - 68)/68 = 0.16382 = 16.38% Excess return: E(rx)(actual) - E(rx)(fair) = 16.38% - 13.54% = 2.84% excess return Price is low, the return is high

Ch 12 Q8 A stock has a beta of 0.85, the expected return on the market is 11 percent, and the risk-free rate is 3 percent. What must the expected return on this stock be?

Er = 0.03 + 0.85*(0.11-0.03) Er = 9.8%

Ch 12 Example: P0(actual) = 67.50 E(P1) = 75 E(D1) = 0.16 B(actual) = 1.74 Rf = 0.015 MRP = 0.08 What is the expected actual return? E(r)(actual) =? What if the expected fair rate of return? E(r)(fair) = ? What is the excess return? What does the excess return mean? What is the fair price of the asset? P0(fair) = ? Is the asset over or under priced? Should an investor buy this asset?

Expected actual return: E(r)(actual) = (75 + 0.16 - 67.50)/67.50 = 11.35% Expected fair rate of return: E(r)(fair) = 0.015 + 1.74*0.08 = 15.42% Excess return: 11.35% - 15.42% = -4.07% This means that the HPR is too high Fair price: P0(fair) = (75+0.16)/(1 + 15.42%) = 65.1187 67.50 - 65.1187 = 2.38 over priced Should not buy assets that are overpriced.

Ch. 10 How is duration used to measure interest rate risk?

For every percentage change in the yield (up/down), the value of the portfolio goes up/down by the duration. For example, if duration is 8.15, then for every percent the yield goes up or down, the value of the portfolio goes up or down by 8.15%.

Ch 12 Q21 Landon Stevens is evaluating the expected performance of two common stocks, Furhman Labs, Inc., and Garten Testing, Inc. The risk-free rate is 4 percent, the expected return on the market is 11.5 percent, and the betas of the two stocks are 1.2 and 0.9, respectively. Stevens's own forecasts of the returns on the two stocks are 13.75 percent for Furhman Labs and 10.50 percent for Garten. Calculate the required return for each stock. Is each stock undervalued, fairly valued, or overvalued?

Furhman: 0.04 + 1.2*(0.115 - 0.04) = 0.13 < 0.1375, undervalued Garten: 0.04 + 0.9*(0.115 - 0.04) = 0.1075 > 0.1050, overvalued If the forecast if less (greater) than the required rate of return, then it is overvalued (undervalued).

Ch. 10 What should a bond portfolio manager do about anticipated changes in interest rates using portfolio duration to maximize returns?

If managers predict rates will go up, they will want more maturities to reinvest at those higher rates. They will probably want shorter durations. If they expect rates to go down, they will want more money locked in for longer periods on time and for a higher duration. They want more duration, higher interest rate risk If they are unsure of which direction rates will go, they can create a balance. They can make sure to have some ability to reinvest to offset prices. They do this by having assets with different maturities all the time. If rates go up, the price of the bond goes down, but they have coupon payments to reinvest at a higher rate and offset the decrease in bond price. If prices go down, then the increase in bond prices will offset the lower return received from the reinvestment of coupon payments. Price risk and reinvestment risk move in opposite directions.

Chapter 12 What is the relationship between price and expected return?

If the market is efficient, the price reflects the level of risk, and therefore, the expected return. The higher the return, the lower the price. Underpriced, should invest. The lower the return, the higher the price. Overpriced, should not invest

Ch. 10 What's a floating interest rate?

Interest rates that are not fixed

Chapter 12 What is the Security Market Line?

It is the line that shows the relationship between the risk and return.

Ch 12 Know how to calculate: Beta and beta of a portfolio Example Problem: Rf = 0.02 E(rm) = 0.09 What is MRP? Betas for the different investments: A = 0.85 B = 1.72 C = 1.04 Amounts invested: A = 4,000 B = 1,000 C = 5,000 Total = 10,000 What is the expected fair rate of return? E( r )(fair) = ? What is the beta of the portfolio? What is the expected return on the portfolio? E(rp) = ?

MRP = 0.09 - 0.02 = 0.07 A = 0.02 + 0.85*0.07 = 0.0795*(4,000/10,000) = 0.0318 B = 0.02 + 1.72*0.07 = 0.1404*(1,000/10,000) = 0.014 C = 0.02 + 1.04*0.07 = 0.0928*(5,000/10,000) = 0.0464 Total E(r)(fair) = 0.0318 + 0.014 + 0.0464 = 9.22% Beta of portfolio: (0.4*0.85) + (0.1*1.72) + (0.5*1.04) = 1.032 Expected return on the portfolio: rf + Bp(E(rm) - rf) 0.02 + 1.032*0.07 = 9.22%

Ch. 10 How is a bond portfolio immunized?

Matching duration of liabilities with the duration of assets. When duration for both assets and liabilities are the same, then there is immunization from interest rate risk.

Ch. 10 Know how to calculate: Bond payments and /or maturity from given prices and yield

Maturity are the years stated until face value is due. If the bond pays semi-annually, then it is the years*2. Bond payments are calculated by the coupon rate*FV. If it is semi-annual, we divided this payment by 2.

Ch 10 Q5 A bond sells for $902.30 and has a coupon rate of 6 percent. If the bond has 12 years until maturity, what is the yield to maturity of the bond?

N = 12 x 2 = 24 I = ? 3.62 x 2 = 7.23% = YTM PV = -902.30 PMT = 6% x 1,000/2 = 30 FV = 1,000

Ch 10 Q1 Aloha Inc. has 7 percent coupon bonds on the market that have 12 years left to maturity. If the YTM on these bonds is 9.1 percent, what is the current bond price?

N = 12x2 = 24 I = 9.1/2 = 4.55 PV = ? -848.55 PMT = 7%x1,000/2 = 35 FV = 1,000

Ch 10 Q2 Rolling Company bonds have a coupon rate of 4 percent, 14 years to maturity, and a current price of $1,086. What is the YTM? The current yield?

N = 14x2 = 28 I = ? 1.62 x 2 = 3.23 = YTM = 3.23% PV = -1,086 PMT = 4%x1,000/2 = Fv = 1,000 CY = 40/1,086 = 3.683%

Ch 10 Q12 Great Wall Pizzeria issued 10-year bonds one year ago at a coupon rate of 6.20 percent. If the YTM on these bonds is 7.4 percent, what is the current bond price?

N = 18 I = 3.7 PV = ? -922.16 PMT = 31 Current bond price = $922.16

Ch 10 Q11: Ghost Rider Corporation has bonds on the market with 10 years to maturity, a YTM of 7.5 percent, and a current price of $938. What must the coupon rate be on the company's bonds?

N = 20 I = 3.75 PV = -938 PMT = ? 33.03835 FV = 1,000 X*1,000/2 = 33.03835 33.03835*2/1000 = 6.61% = coupon rate

CH 10 Zero-coupon bond examples Maturity = 10 years YTM = 6% semi-annual FV = 1,000 What the payment and present value?

N = 20 I/Y = 3% PMT = 0, because 0 coupon bonds FV = 1,000 PV = 553.68

Ch 10 Q6 A bond with a maturity of 12 years sells for $1,047. If the coupon rate is 8.2 percent, what is the yield to maturity of the bond?

N = 24 I = ? 3.80 x 2 = 7.6% = YTM PV = -1,047 PMT = 8.2% x 1,000/2 = 41

Ch 10 Bond practice: M = 13 years Semi annual YTM = 7.125 P0 = 968.55 CR = ? CY = ? Is this bond a discount or a premium?

N = 26 I = 7.125/2 = 3.5625 PV = -968.55 PMT = ? 33.75 (per 6 months) FV = 1,000 33.75 = 1,000*x = 0.03375*2 = 6.75% = CR CY = 67.50/968.55 = 6.97% 7.125% > 6.97% > 6.75% Discount

CH 10 Bond practice problem: FV = 1,000 P0 = 1,040 M = 20 years CR = 6% semi-annual YTM = ? CY = ? Is this a premium or a discount?

N = 40 I = 2.83%*2 = 5.66% = YTM PV = -1,040 (this has to be negative) PMT = 1,000*6%/2 = 30 FV = 1,000 CY = 60/1040 = 0.05769 6%>5.77%>5.66% This a premium bond

Ch 10 Q8 Atlantis Fisheries issues zero coupon bonds on the market at a price of $417 per bond. Each bond has a face value of $1,000 payable at maturity in 20 years. What is the yield to maturity for these bonds?

N = 40 I = ? 4.42% = YTM PV = -417 PMT = 0 FV 1,000

Ch 10 Example problem: FV = 1,000 coupon rate = 6% YTM = 6% semi-annual Maturity = 20 years What is the present value? Is this bond sold at a discount/premium/par? What is the PV if the YTM increased by 0.5%? What is the PV if the YTM decreased by 0.5%? Was there more gain or more loss? Which one had more gain/loss? Was it the premium/discount?

N = 40, IY = 3, PMT = 30, FV = 1,000, PV = 1,000 Sold at par. 0.5% increase N = 40, IY = 3.75, PMT = 30, FV = 1,000, PV = 944.48 Discount. Loss of 55.52 0.5% decrease N = 40, IY = 2.75, PMT = 30, FV = 1,000, PV = 1,060.20 Premium. Gain of 60.20. The gain on the premium is larger than the loss in discount.

Ch 10 Q13 Soprano's Spaghetti Factory issued 25-year bonds two years ago at a coupon rate of 7.5 percent. If these bonds currently sell for 108 percent of par value, what is the YTM?

N = 46 I = ? 6.81% = YTM PV = -1080 PMT = 37.5

Ch 10 Q4 A bond with 25 years until maturity has a coupon rate of 7.2 percent and a yield to maturity of 6 percent. What is the price of the bond?

N = 50 I = 6/2 = 3 PV = ? -1,154.38 PMT= 7.2% x 1,000/2 = 36 FV = 1,000 Price = $1,154.38

Ch 10 Q3 A bond has a coupon rate of 8.2 percent and 9 years until maturity. If the yield to maturity is 7.4 percent, what is the price of the bond?

N = 9 x 2 = 18 I = 7.4/2 = 3.7 PV = ? -1,051.89 PMT = 8.2% x 1,000/2 = 41 FV = 1,000 Price = $1,051.89

Ch 10 Q7 May Industries has a bond outstanding that sells for $928. The bond has a coupon rate of 7.5 percent and nine years until maturity. What is the yield to maturity of the bond?

N = 9 x 2 = 18 I = ? 4.33 x 2 = 8.67% = YTM PV = -928 PMT = 7.5% x 1,000/2 = 37.5

Ch 10 Bond problem: P0 = $974.16 CR = 4% semi annual YTM = 4.25% M = ?

N = ? 27.51/2 = 13.76 years I = 4.25/2 = 2.125 PV = -974.16 PMT = 4%/2 = 2%*1,000 = 20 FV = 1,000 This is a discount

Ch 12 Q11 Asset W has an expected return of 12.0 percent and a beta of 1.1. If the risk-free rate is 4 percent, complete the following table for portfolios of asset W and a risk-free asset. Illustrate the relationship between portfolio expected return and portfolio beta by plotting the expected returns against the betas. What is the slope of the line that results? Percentage of the portfolio in Asset W: 0% 25 50 75 100 125 150

Portfolio expected return: 0%(0.12) + 1(0.04) = 4% 0.25*0.12 + 0.75*0.04 = 6% 0.5*0.12 + 0.5*0.04 = 8% 0.75*0.12 + 0.25*0.04 = 10% 1*0.12 + 0 = 12% 1.25*0.12 - 0.25*0.04 = 14% 1.5*0.12 - 0.5*0.04 = 16% Portfolio beta: 0*1.1 + 0*100 = 0 0.25*1.1 = 0.275 0.5*1.1 = 0.55 0.75*1.1 = 0.825 1*1.1 = 1.1 1.25*1.1 = 1.375 1.5*1.1 = 1.65

Ch. 10 What is the relationship between YTM, coupon rate, and current yield if a bond is selling at a premium?

Present Value is greater than the Face value. Coupon rate is greater than the market rate (rate of return). CR > CY > YTM If the bond is selling at a premium the coupon rate is higher than the market rate.

Ch 10 What is the relationship between YTM, coupon rate, and current yield if a bond is selling at a discount?

Present value is less than the face value Coupon rate is less than the market rate (rate of return). YTM > CY > CR The discount has to make up for the fact that the coupon rate doesn't equal the market rate. If the bond is selling at a discount, the market rate has to be greater than the coupon rate.

Ch. 10 What is the difference between price risk and reinvestment risk?

Price risk is what we refer to when talking about interest rate risk. Changing asset values due to changing interest rates. Price of bond changes with changing interest rates. When interest rates are down, the price of the bond goes up. When rates are up, the price of the bond goes down. Reinvestment risk refers to the inability to maintain return on periodic cash flow in the face of changing interest rates. When investors receive coupon payments from bonds, they might not get a good return in the payments are reinvested when interest rates are down. When interest rates are up, then there may be good return.

Ch What is the difference between registered and bearer bond ownership?

Registered means your name is attached to the bond. The company knows who owns the bonds. Can make payments straight to the person. If the bond certificate/coupons are lost, the company has record of the registered owner. Harder to commit tax fraud. Bearer bonds don't have a name attached. People have to physically go to a financial institution to redeem their bond payments. If the certificate is lost/stolen, can't confirm the identity of the owner. Easier to commit tax fraud.

Ch 10 What is a trust bond

Secured by collateral. This type of bond is rare.

Ch 12 Q12 Stock Y has a beta of 1.05 and an expected return of 13 percent. Stock Z has a beta of 0.70 and an expected return of 9 percent. If the risk-free rate is 5 percent and the market risk premium is 7 percent, are these stocks correctly priced?

Stock Y: 0.05 + 1.05*0.07 = 0.1235 < 0.13, undervalued Stock Z: 0.05 + 0.7*0.07 = 0.099 > 0.09, overvalued

Ch 10 What does it mean when a bond is callable?

The issuer can pay off the bond early. The market will usually demand a higher interest rate for this bond.

Chapter 12 What is the 'reward' for bearing higher risk in the competitive market?

The reward for bearing higher risk in the competitive market is a greater rate of return

Ch. 10 What is the interest rate risk?

The value of a financial instrument can be affected by changing interest rates in the marketplace. The possibility of bond prices going up or down when market rates change. When rates go down, prices goes up. When rates go up, prices go down. When you buy a bond, if interest rates go up, you lose the market value of the bond. If interest rates go down, you gain market value.

Ch 10 What is a zero coupon bond?

There are no coupon payments. Pays only the face value at maturity. Investor return come from buying the bond at a discount from its face value. Investor pays the present value and bond issuer pays the face value at the end. Zero coupon bonds can be artificially in the secondary market. Private investment firms dismantle bonds and sell them to investors with just one payment.

Ch. 10 How is price volatility related to length of time until maturity?

There is more price volatility/interest rate risk with bonds that have longer maturities (long-term bonds).

Ch 10 What is a debenture bond?

This is an unsecured bond. Most common. As long as the firm maintains financial health, they will promise to make payments.

Ch 10 What is the face/par value?

This is the value of the bond listed on its certificate. What the bond is worth

Ch. 10 What is meant by yield-to-maturity (YTM)?

Total annualized return assuming no default and coupon reinvestment. Interest rate that the bondholder will earn based on what was paid for the bond v. what the bond promises to pay.

Ch. 10 What is a bond?

When an investor gives money to the government or a corporation. With bonds there is a promise being made on certain dates with certain amounts of payment with some exceptions.

Ch. 10 Know how to calculate: Bond price and bond YTM Example: A bond matures in 12 years. There is a 4% coupon rate. The rate of return/market rate is 3.5%. The price of the bond is $1,000. This bond pays semi-annually. What is the YTM? What is the present value of the bond? Is it a premium or a discount? What is the current yield?

YTM = 3.5% N = 24 I/Y = 3.5/2 = 1.75 PMT = 20 FV = 1,000 PV = 1,048.65 Premium 40/1,048.65 = 3.8%

Ch. 10 Know how to calculate: Bond price and bond YTM Example: A bond matures in 12 years. There is a 4% coupon rate. The rate of return/market rate is 5%. The price of the bond is $1,000. This bond pays semi-annually. What is the YTM? What is the present value of the bond? Is it a premium or a discount? What is the current yield?

YTM = 5% N = 12*2 = 24 I/Y = 5/2 PMT = 4%*1,000/2 = 20 FV = 1,000 PV = 910.58 It is a discount because 910.58 < 1,000 $40/910.58 = 4.4% - current yield

Ch 12 Q10 A stock has a beta of 0.9 and an expected return of 9 percent. A risk-free asset currently earns 4 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of 0.5, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta? d. If a portfolio of the two assets has a beta of 1.80, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.

a. (0.09+0.04)/2 = 6.5% b. 0.5 = (x)(0.9) + (1-x)(0) 0.5/0.9 = 0.55556 = x 1-0.55556 = 0.4444 for risk free & 0.55556 other stock c. 0.08 = 0.09*x + 0.04(1-x) 0.08 = 0.09x + 0.04 - 0.04x 0.04 = 0.05x x = 0.8 B = 0.8*0.9 + 0.2*0 = 0.72 d. 1.8 = 0.9x + 0(1-x) x = 2 risk free weight is -1 They invested 200% in the stock and -100% in the risk free asset. This means they are borrowing from the risk free asset to invest in the other stock.

Chapter 12 What is beta?

beta is a proportional level of systematic risk it is a reaction coefficient

Chapter 12 What does beta measure?

beta measures systematic risk

Ch 10 What does it mean when interest rates are asymmetrical?

interest rate risk is asymmetrical, meaning if rates were to go down, we would gain more than the absolute value of what we would lose if the interest rates went up by the same percentage.

Ch. 10 Will a bond price rise more for a given % rate decrease, or fall more for the same % increase?

it will rise more for a given % rate decrease than fall for the same % rate increase. For the same amount of percentage increase that YTM goes up/down, the gain will be greater than the loss This happens because the interest rate risk is asymmetrical.

Ch 10 What types of trends represent interest rate risk?

non linear and asymmetrical

Ch. 10 What is bond portfolio immunization?

preventing interest rate risk from affecting investments in bonds

Ch 10 What is the coupon rate?

promised rate of interest.

Chapter 12 Know how to calculate: Expected return from CAPM What is the equation?

risk-free rate + beta * (expected return on the market - risk free rate)

Chapter 12 What is the beta of the risk-free asset?

the beta of a risk-free asset is 0

Chapter 12 What is the beta of the market?

the beta of the market is 1

Ch 12 Portfolio Beta: Beta: X = 1.25 Y = 0.78 Z = 1.32 Investment X = 4,000 Y = 500 Z = 500 What is the portfolio beta?

total investment = 4,000 + 500 + 500 = 5,000 X = 4,000/5,000 = 0.8 Y = 500/5,000 = 0.1 Z = 0.1 Beta: (1.25*0.8) + (0.78*0.1) + (1.32*0.1) = 1.21