HW4

Fall 2017

Fixed Income Markets and Derivatives

1.You are provided with the following quote on Settlement date is October 1, 2013. All quoted prices are in decimals.

Maturity	Coupon	Bid	Asked	Chg	Asked yield
3/31/2015	0.250	100.0273	100.0508	-0.0234	0.216
3/31/2015	2.500	103.3789	103.4023	-0.0273	0.218
4/15/2015	0.375	100.1914	100.2148	-0.0234	0.235
4/30/2015	0.125	99.7813	99.8203	-0.0234	0.239
4/30/2015	2.500	103.5273	103.5508	-0.0352	0.245

Compute the following for each of the above bonds and provide an interpretation:

a)PVBP

b)Use excel to compute Duration

c)Modified Duration

2.I have attached one articles from Wall Street Journal:

a.Duration risk.pdf

the article contains questions marked in Red color. Please answer those questions.

ARTILCE A-

Investors looking for big, bold returns in government bonds could have found them in two very different places over the past year: Venezuela and Japan. Venezuelas case is a familiar story to those who rummage around the dicier corners of the bond market: There were substantial questions about whether Venezuela would have the cash to repay a bond that came due on Feb. 26. It did, and an investor who took the risk of buying it a year earlier would have earned a 27% return. Japan is less obvious, and it highlights a quiet risk suffusing bond markets in the era of low and negative rates: duration. The duration of a bond is a measure of when an investor gets his or her money back. Longer-term bonds have higher durationas do bonds with lower coupon payments, because low coupons mean more waiting. Today, with global interest rates extraordinarily low, and borrowers issuing ultralong debt, duration is shooting up. EXPLAIN WHY THIS IS SO.

Duration implies risk: A rule of thumb is that a one percentage-point change in interest rates implies a change in the bonds price equal to the duration. A bond with a duration of 25 years will jump 25% if interest rates fall by one percentage pointand fall 25% if rates rise by the same amount. Japanese debt is a prime example. EXPLAIN WHY THIS IS SO

Last year, Japan issued a 40-year bond with a coupon of 1.4%. Rates have fallen in Japan, and so the price has risen 34%. As durations get longer, risks mount. France on Tuesday issued a 50 year bond with a coupon of 1.75%. Before the eurozone debt crisis, France was issuing similar bonds with coupons of 4%. IS THIS BOND MORE RISKY THAN JAPAN'S BOND? EXPLAIN WHY OR WHY NOT.

An investor who bought the earlier bond would get his or her money back in the form of coupon payments much fastercollecting the face value of the bond in 25 years. An investor who bought on Tuesday wouldnt collect enough coupons to recoup the face amount before the bond matures. WHAT DOES THIS SENTENCE MEAN?

That long waiting period is worrisome. An educated investor can take a guess at where interest rates might be in two or three years and the situation that the economy might be in then. That is the sort of range that many central banks and other large institutions attempt to forecast across, and many end up being inaccurate. A forecast of the world in four decades is a fools errand. Usually, to account for duration risk, the yield curve on bonds is relatively steep. That means bonds with long maturities have considerably higher yields, since an investor is facing considerable uncertainty. HOW DOES A STEEPNING YIELD CURVE ACCOUNT FOR DURATION RISK?

In Japan and increasingly in Europe, yield curves are flattening. Investors who usually might have opted for shorter-dated government bonds in Japan have been driven into more distant maturities. The yield on a 40-year Japanese bond has declined from above 2%, when Prime Minister Shinzo Abe s adventurous economic stimulus began in late 2012, to around 1.5% at the end of 2015. Since the Bank of Japan 8301 0.14 % s negative rate announcement, it has plunged to below 0.5%. Few are predicting a turnaround in Japanese rates any time soon. But 40 years is a long time to wait, and if rates do turn, investors holding the bond will be in troubleeven though Japans government debt is regarded as some of the worlds safest. If rates rise, a bond yielding 0.49% becomes unattractive, and an investor must take a loss to sell it. Though the flatter yield curves are a consequence of monetary stimulus designed to give the economy a boost, they are also a major problem for financial institutions that make their profit in the window between short-term liabilities and long-term assets. In February, the largest net buyers of Japanese government bonds with maturities over 10 years were Japanese insurance companies, according to Shuichi Ohsaki, chief rates strategist at Bank of America Merrill Lynch in Japan. Insurance companies, particularly life insurers, need long-term assets to match their long-term liabilities. The European Central Bank cut its official deposit rate into negative territory in 2014, reducing it to minus 0.4% and expanding its quantitative easing, or QE, program in its March meeting this year. And duration has risen steadily in Europe. The duration of the iBoxx euro sovereign index, which tracks eurozone government bonds, has risen to 7.2 years, according to financial data firm Markit. Thats up from less than five years in 2006 and about six years until as recently as 2011. WHAT DOES THIS TELL YOU ABOUT EUROPEAN GOVERNMENT DEBT? Still, prodding investors out of the market for sovereign debt is a main goal of Europes and Japans monetary easing. But institutions which have made government bonds the backbone of their business model, like insurance companies and pension funds, may struggle to find safe alternatives with a similar yield. Those investors and fund managers are forced to take on more risk. When that is through credit risk, as in the case of Venezuelan government bonds, it seems obvious to everyone. When they are loading up on bonds that dont mature for longer and longer periods, it is less easy to see. But the risk is still there and growing.