Study Guide Blaw 372

Module 1

Understand the importance of fixed-income markets. How do fixed-income markets compare to stock markets?

• Importance of fixed income markets:

• Large relative to equity markets – larger amount outstanding, new securities issued, and assets held by the US financial sector

• Fixed income markets vs. stock markets:

• Fixed income securities promise a fixed stream of income unlike stocks. Equity is handed out in dividends, not payments. Equity is ownership.

Be familiar with the characteristics of fixed-income securities. There is a lot of vocabulary here, so make sure you are comfortable with it.

• Fixed income securities – debt securities or preferred stock.

• Debt securities: money market securities and bonds

• Money market: short term (<1 year), low risk, ex. T-bills, CDs, commercial paper
• Bonds: long term (>1 year), safe to risky, ex. t-bonds, TIPS, municipals, corporate bonds, mortgage-backed securities

• LIBOR rate: rate at which the highest credit quality banks trade at in London. Used as a RR.
• Amortization: principal of a bond repaid over the life of the bond. Uses average life instead of maturity. Ex. mortgages and auto loans.
• Embedded options: callable, putable, convertible, exchangeable
• CUSIP: committee on uniform security identification procedures, 9 character number, first 6 digits identify issuer, next digits identify specific bond/sec.
• Short sell- selling something you don’t own, you’ll have to buy it back later bc you borrowed it. You hope to buy it back at a lower price.
• Accrued interest: proportion of the next coupon payment due to the seller for the length of time she held the bond

Know all of the time-value-of-money calculations for floating-rate securities. In other words, be able to solve for quoted margin, discount margin, years to maturity, and price. Be comfortable with more than just annual coupons – semi-annual, quarterly, maybe monthly?

• Discount margin: average margin over the RR that the investor can expect to earn over the life of the security

• Calculated as the margin that would make the PV of the CFs = to price
• CFs based on current value of the RR
• I/Y – LIBOR = DM (in bps)

• Solve for Y, subtract off the LIBOR, = bps

• Quoted margin: = the basis points

• QM + RR equivalent to CR

• Discount margin:

• DM + RR equivalent to YTM

Understand the relationship between coupon rate, yield to maturity and price for a fixed-coupon security. When would the security be selling at a premium/discount/par? Similarly, understand the relationship between quoted margin, discount margin and price for a floating-rate security.

• Price max: because YTM can’t be < 0. Sum of all CFs without discount is price.
• Par = market yield = coupon rate
• Premium = required yield < CR
• Discount = required yield > CR
• Floating rate securities:

• Quoted margin: = to CR

• QM < DM = discount
• QM > DM = premium

• Discount margin: = to YTM

Be able to calculate accrued interest and understand why it matters. Also, be able to calculate the clean and dirty price of a bond that trades between coupon payments. Which price tells you the amount of money that actually changes hands on the settlement date?

• AI = payment * time convention
• CP = DP – AI
• Clean: price you’re quoted to pay, DP: price you actually paid
• Time conventions:

• Treasuries: actual day count
• Corporations/municipals: 30/360 day count

• Why it’s important?

• Important because as the seller, you are owed the interest built up on the coupon in between the last coupon date and the date you sell it.

Be able to calculate current yield, yield to maturity, yield to call, yield to put, and yield to worst. What are the limitations of each one as a measure of a bond’s expected performance?

• Current yield = annual dollar coupon payment/price

• Limits: doesn’t take into account other forms of income, TVM is ignored

• YTM = interest rate that makes PV of CFs = to price

• Limits: only good if held to maturity, assumes you reinvest at the same rate

• YTC = same as YTM, only take into account payments before call date

• Limits: same as YTM limits

• YTP = same as YTM

• Limits: same as YTM

• YTW = the lowest of all yields (YTM, YTC, YTP)

Understand how one would structure a floater and an inverse floater from a fixed-coupon bond. That is, be able to solve for the coupon on the floater, given the coupons on the collateral and the inverse floater. Or be able to solve for the coupon on the inverse floater, given the coupons on the collateral and the floater. Understand how a floor on the inverse floater affects the cap on the floater, and vice versa.

• Floor on the inverse floater, cap on the floater

• To make sure investment payment isn’t negative
• Solve for cap by setting RR to 0 on inverse floater

• Coupon payments and par values of the floaters must sum up to the par values and payments of the collateral bond

Be able to calculate a bond’s return and annualize it on a bond-equivalent basis.

• Steps:

• 1. Compute total coupon payments + interest on interest

• FV[PV=0]

• 2. Determine projected sale price at end of investment horizon

• Price = PV[remaining CFs discounted at projected yield]
• PV[Y= projected yield, FV=100]

• 3. Add step 1 and step 2 together

• = Wealth at the end of the investment horizon

• 4. = [Total future dollars/purchase price]^1/h -1

• h = number of 6 month periods in investment horizon

• 5. Multiply by 2 for APR

Module 2

Be able to calculate the Macauley duration, modified duration and convexity of a debt security either via exact expressions or approximation expressions.

• MD = weighted average maturity of the CFs of a fixed-income security

• = Sum [PV(Ct)/Price * t]
• Divide sum by 2 for years
• For fixed-rate bonds without embedded options:

• Average time it takes you to recover your CFs

• For a fixed-coupon rate bond

• Duration will never be more than the maturity
• It will equal the maturity if it’s a zero coupon bond

• Modified Duration = D/(1+Y)  Y=per period yield, D=MD in years

• Estimated % price increase for a 1% drop in yields
• More intuitive than MD
• Change in P if y increases by 1% = (modified duration)(dy)
• Change in dollars? (modified duration percentage in decimal form)(initial price)

• Convexity = formula given to us on exam

• Calculated in half-years, so divide by m squared to adjust to years (m= number of coupons per year)
• Higher number means higher curvature in p/y relationship

• Approximations:

• Duration

• = (P_ - P+)/[2(P0)(change in y)]
• Start with P0 + y. increase y by x bp, calculate P+. Decrease y by x bp, calculate P_. Change in y is the x bps change in y.

• Convexity:

• = (P+ + P_-2P0)/[P0(change in y)^2]
• same steps as above

Be able to use duration and/or convexity to predict the effect that a given change in interest rates will have on the price of a debt security. Be able to calculate the actual price change and compare it to the duration-predicted price change. Based on this be able to draw conclusions about the convexity of the debt security.