FI: Yield Measures, Spot & Forward Rates

Question 1

3 sources of income from a bond =

Answer 1

1. periodic coupon payments
2. repayment of priincipal, including capital gains/losses
3. reinvestment income earned from reinvesting periodic coupon payments

Question 2

Current yield =

Answer 2

= annual cash coupon payment/bond price

does not give any information about principal repayment and reinvestment income

Question 3

YTM =

Answer 3

annualized internal rate of return based on bond’s cash flows and price.

Make sure to multiply ‘i’ by 2 if the calculation is for a semiannual coupon payment.

Question 4

Relationship between coupon/CY/YTM =

Answer 4

Question 5

Bond Equivalent Yield (BEY) =

Answer 5

aka semiannual (pay) YTM

just a regular YTM - for a semi annual coupon the BEY is 2x semi annual discount rate.

note: for zeros it is customary to calculate BEY (treat as a semi annual pay bond with PMT 0)

Question 6

Annual pay YTM =

Answer 6

as opposed to BEY - one coupon payment per year, simply the IRR of the expected annual cash flows.

Question 7

Yield to call =

Answer 7

to calculate yield on a callable trading at a premium.

the YTC may be less than the YTM in this case.

FV = call price

n = semiannual periods until call date

BONDS ARE QUOTED ON A YTC BASIS WHEN YTC IS LESS THAN YTM - CAN ONLY BE THE WHEN THE BOND IS TRADING AT A PREMIUM

Question 8

YTW =

Answer 8

WORST OUTCOME.

could be YTM, YTC, YTfirst par call

Question 9

Yield to refunding =

Answer 9

same as a YTC except uses the period up to the end of protection from refunding (bond may be callable but not able to be refunded, so the issuer doesn’t call until the first refundable date)

Question 10

YTP =

Answer 10

if a bond has a put feature and is selling at a discount.

YTP will likely be GREATER than the YTM

This is all opposite of YTC

Question 11

CFY - cash flow yield =

Answer 11

used for MBS and other amortizing asset backed securities with monthly cash flows.

takes a monthly schedule of expected cash flows (considering likely prepayments) and calculates a MONTHLY INTERNAL RATE OF RETURN

The formula compounds the 6 monthly cash flows into a semi annual discount rate which we double to get the BEY

Limitation is that prepayments may differ from the model.

Question 12

Limitations of yield measures =

Answer 12

assume that payments can be reinvested at YTM - if they are actually invested in a lower rate, the REALIZED YIELD will be lower.

Question 13

Calculating reinvestment income required =

Answer 13

if we know how much compound return we require, we can take the interest and principal payments and back into the amount of reinvestment income we need.

ie 6% semiannual pay 10yr 1000 par.

1000(1+0.03)^20 = $1806.1

$1000 par + 20x30 coupon payments + REINVESTMENT INCOME = 1806.1

Question 14

Factors affecting reinvestment risk =

Answer 14

HIGHER COUPONS - more cash flow to reinvest

LONGER MATURITIES - more of the total value of the investment is int he coupon cash flows (and subsequent interest earned)

Question 15

Semi annual vs annual return, and converting =

Answer 15

to convert a semi annual pay (BEY) we divide by 2 to get the semi annual yield - then compound this ^2 to get the annual yield (EAY)

DO THE REVERSE TO GO FROM ANNUAL TO SEMI ANNUAL

annual rate ^(1/2) x 2

Question 16

Bootstrapping =

Answer 16

by knowing the yields on zero coupon treasuries we can back into the spot rates of the theoretical treasury spot rate curve.

We take the YTM as the spot rate for the first zero (with one cash flow)

we use this as the spot rate for discounting the first cash flow of the 2 period treasury, and solve for the discount rate of the second cash flow (given that price is par due to the arbitrage free nature of the yield curve)

BE SURE TO ADJUST AS NECESSARY FOR THE YIELDS GIVEN - MAY BE SEMIANNUAL YTM WITH SEMI ANNUAL CASH FLOWS, SO YTM HAS TO BE DIVIDED BY 2

Question 17

Nominal spread =

Answer 17

an issue’s YTM - similar maturity tsy YTM

drawback: YTM uses a single discount rate to value cash flows, ignoring the shape of the spot curve

(YTM for a coupon bond is theoretically correct only if spot rate curve is flat - ie, that we can discount all cash flows of the bond at the same rate)

Question 18

Z-spread =

Answer 18

aka zero volatility spread/static spread

Take the treasury spot yield curve

if we discount a risky bond at these rates, the PV will be too high given the risk –> we need to discount at a higher rate

the Z SPREAD is the spread we add on to EACH NODE OF THE TREASURY SPOT YIELD CURVE to discount the risky bond’s cash flows back to a PV equal to its market price

Question 19

Factors affecting the difference in nominal and z spreads =

Answer 19

a) the steeper the benchmark spot rate curve, the bigger the difference between the two spreads (the z spread will be bigger when the benchmark curve is positively sloped)

–> when the spot rate curve is flat there is no difference

b) the earlier the bond principal is paid , the greater the difference between the two spread measures.

ie the spread difference for an amortizing MBS will be greater than that of a coupon bond.

Question 20

OAS =

Answer 20

= spread to the treasury spot rate curve that the bond would have if it were option free

shows the compensation for non option characteristics - credit risk, liquidity risk, interest rate risk

Question 21

Option cost (in percent) =

Answer 21

= Z spread - OAS

as the OAS takes out the compensation for the option, and the Z spread does not.

the option cost here is how much the holder of the bond will be compensated for the issuer having the call option.

THIS IS OPPOSITE FOR A BOND WITH A PUT OPTION

Question 22

Forward Rate =

Answer 22

borrowing/lending rate for a loan to be made in the future.

notation is the length of loan, then when in the future it will be made

Question 23

Rship between FORWARD and SPOT rates =

Answer 23

spot rates should be equal to the (geometric) average of the intermediate forward rates

so borrowing at the 3yr spot rate should be the same as borrowing at the 1 yr spot AND the 1y1y AND the 1y2y

the arithmetic average of the forward rates will give a good approximation; the geometric average calculation is below: