Yield curve

Question 1 (15 marks)
a) (8 marks) Above is the US yield curve in 2007 and 2011. Using the theories of the
term structure of interest rates, explain the shape of the yield curve for Figures 1 and
2. Give a brief explanation of the US economy for each of those time periods that
may explain what the yield curve is predicting. You may need to do a little research
to answer this question. (Your answer is not to exceed 8-10 lines!)
b) (7 marks) In February 2018, the Dow Jones industrial average shed nearly 2,300
points (approx. 9%) with emphasis on Monday, Feb. 5th.
Following is a quote regarding the stock market downturn in February 2018:
” … the markets are worried that the U.S. Federal Reserve has badly underestimated
inflationary pressures coming from the long-booming U.S. labour market, which it let
run too hot for too long through its years of low-interest-rate policy. That suggests the
Fed is behind the curve on raising interest rates to tame inflation, and will have to pick
up the pace in the coming months – which would slam the brakes on stock values and
the economy”
Posted on Quercus, the article ” Flat U.S. yield curve not signaling recession risk:
Yellen” former Fed. Reserve Chair Janet Yellen references the current flat US treasury
curve. That article references the slope between the 2yr/10 yr US treasuries and the
slope between 5yr/30yr US treasuries.
Do you agree or disagree with the above quote regarding inflation as the cause of the
stock market sell-off? Your argument should by supported by both the hypothesis on the
shape of the yield curve as referenced by Yellen in the posted newspaper article and the
observed treasury yield slope between the 2s/10s and 5s/30s both in December 2017
and after the stock market sell-off in February. You can obtain historical US treasury
yields from the U.S. Department of the Treasury. Please indicate the dates of your US
treasury yields. (Your answer is not to exceed 8-10 lines!)
Question 2 (5 marks)
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Please use the Government of Canada bond data provided in Appendix A. The yield to
maturity levels are as of September 11th, 2018. Assume this is the date the coupon will
be set.
A BBB-rated company is contemplating issuing 2 bonds:
1. Bond 1 that matures on September 11th, 2021 and,
2. Bond 2 that matures on September 11th, 2025
The credit spread is +237 bps for Bond 1 and +332 bps for Bond 2.
Please calculate the coupons (to 3 decimal places) on Bond 1 and Bond 2 as of
September 11th, 2018. For each calculation, state which bonds you are using for your
calculations and why and whether you are using bid side or ask side yields. (maximum
2-3 sentences).
Question 3 (15 marks)
An investor purchases the following bonds for his portfolio and the settlement dates are
given for each transaction.
For each bond position calculate the accrued interest to the settlement date and the total
purchase price (market price plus accrued interest) paid by the investor.
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a) $1 million par value of Bell Canada’s 4.464% bond due April 1st 2048. The bond was
newly created and the interest accrual date is as of March 29th, 2018. The first
coupon will be paid on October 1st, 2018. The investor bought the bonds in the
market at a price of 99.364 per bond. The Bell bond is a USD dollar bond and has
30/360 day count convention. September 13th, 2018 is the settlement date.
b) Now assume that the Bell bond was issued in Canadian dollars and uses an
actual/365 day count convention. What is accrued interest now? What is the dollar
difference in accrued interest versus using the 30/360 day count convention above?
Please ignore the foreign exchange aspect (don’t convert) and assume a September
13th, 2018 settlement date.
c) $1 million par value of a Government of Canada 2.00% bond due June 1, 2028.
The investor bought the bonds in the market at a price of 97.144 per bond. The GoC
bond uses actual/365 day count convention and settles on September 13th, 2018.
d) $1 million par value of a US Treasury 2.875% due August 15, 2028. The
investor bought the bonds in the market at a price of 99.125 per bond. The
US T-bond uses the actual/actual day count convention and settles on
September 12th, 2018.
e) $1,000,000 par value of a Government of Canada 4.25% due December 1,
2021 real return bond. The settlement date is September 13th, 2018. The
Base CPI value, when the bond was auctioned, was 83.077. The Reference
CPI value is 133.88. Assume actual/365 day count convention and calculate
the accrued interest including inflation compensation for this accrued interest.
Question 4 (8 marks)
On May 26th, 2013 Calloway Real Estate Investment Trust (“Calloway”) announced that
it would redeem its $75 million 7.95% Series D senior unsecured debentures due June
30, 2014 (the “Series D Debentures”). The redemption date was set for June 26, 2013.
The bonds were issued on June 30th, 2009 and pay interest semi-annually on June 30th
and December 30th of each year.
From the prospectus: At its option, Calloway may redeem the Debentures at a
redemption price equal to the greater of (i) the Canada Yield Price and (ii) par, together
in each case with accrued and unpaid interest to the date fixed for redemption.
“Canada Yield Price” means a price equal to the price of the Debentures calculated to
provide a yield to maturity, compounded semi-annually, equal to the Government of
Canada Yield plus 1.33%.
Assume the Government of Canada Yield was 1.059%.
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Using the above information, calculate the make whole redemption price per $1,000
(one bond). Please add in any other payments (accrued interest or coupon) separately.
What was the dollar amount of the premium paid for each bond?
Question 5 (7 marks)
On September 21st, 2018 the 5-year GoC bond with a coupon of 2% was quoted at a
clean price of 98.461. The GoC 2% bond has a September 1st, 2023 maturity date.
A bond dealer purchased the bond for settlement on September 25th 2018. He would
also like to finance the bond trade for 1 day (so repo the bond out for 1 day). The repo
settlement date is September 26th, 2018. The repo rate for a term of 1 day is 1.479%.
There is no ‘hair cut’ on this transaction.
Using this information, what is the ‘all-in’ or ‘term’ money borrowed by this dealer on
September 26th, 2018? Be specific as it relates to all the components of the trade
(accrued interest, repo term interest, total settlement value). Show all of your work and
assume actual/365 day count convention.
Flat U.S. yield curve not signaling recession risk:
Yellen
Dan Burns
NEW YORK (Reuters) – For all those market mavens out there fretting about
the relentless flattening of the U.S. Treasury yield curve, Federal Reserve Chair
Janet Yellen has a message for you: Get over it.
U.S. outgoing Federal Reserve Chair Janet Yellen holds a news conference after a twoday
Federal Open Market Committee (FOMC) meeting in Washington, U.S. December
13, 2017. REUTERS/Jonathan Ernst
In response to her final question at her final press conference on Wednesday,
after nearly four years at the helm of the U.S. central bank, Yellen effectively
dismissed the current shape of the U.S. yield curve as little more than a
technical anomaly.
“I think there are good reasons to think that the relationship between the slope
of the yield curve and the business cycle may have changed,” Yellen said.
The yield curve – the plot of all of the yields on Treasury securities of maturities
from 4 weeks to 30 years – has long been studied by economists and investors as
a signal of the health of the economy.
A steep curve, when long-dated yields are substantially higher than shorterdated
ones, is emblematic of a growing economy that is likely to produce
inflation, the biggest driver for yields further out the time-to-maturity curve.
A flat curve, when the gap between the two ends of the curve is narrow, is
typically associated with periods when central bankers are working to combat
inflation by lifting shorter-term interest rates, something the Fed has done five
times now even though signs of inflation are scant.
And an inverted curve, when short-term yields are higher than long-term ones,
has served as a classic precursor of economic recession.
In the last year, the spread between 2-year US2YT=RR and 10-year
US10YT=RR Treasury note yields, a benchmark measure of yield-curve slope,
has collapsed from around 135 basis points to 57 basis points.
Between 30-year bonds US30YT=RR and 5-year notes US5YT=RR, another
widely tracked measure, the spread has narrowed from 127 basis points to 62.
(Graphic: U.S. Treasury yield curve is flattening – reut.rs/2Bmo2zQ)
This has given rise to a lot of chatter in financial markets that the flattening
curve signals the waning days of an economic expansion that dates from mid2009,
following the Great Recession.
“Now there is a strong correlation historically between yield curve inversions
and recessions,” Yellen said. “But let me emphasize the correlation is not
causation.”
Moreover, this time it’s different, Yellen argued.
The current flatness of the yield curve is likely attributable to a lack of
something called “term premium”, or essentially a premium in yield that
investors of long-date bonds demand in compensation for inflation risk. With
little inflation risk, today’s term premium has effectively vanished.
“Right now the term premium is estimated to be quite low, close to zero, and
that means that structurally, and this can be true going forward, that the yield
curve is likely to be flatter than it’s been in the past,” Yellen said.
And, she said, “if the Fed were to even move to a slightly restrictive policy
stance, you could see an inversion with a zero-term premium.”
Yellen’s comments may lift concerns about the yield curve for now, and allow
the Fed under incoming chair Jerome Powell to continue with a gradual path of
rate increases.
But if spreads continue to narrow it is likely to cause tensions with investors and
within the Fed.
Already St. Louis Fed chair James Bullard and others have flagged the risks of a
Fed-induced yield curve inversion as a reason for policymakers to move more
cautiously. Bullard argued recently that the curve could invert within a year if
the Fed continues to hike.”
(GRAPHIC: U.S. core CPI, PCE, fed funds rate – reut.rs/2ACP5ay)