Lecture 3_InterestRatesForwards.pptx

7/27/2019 Lecture 3_InterestRatesForwards.pptx

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Forward Rate Agreements

Session 3Derivatives & Risk Mgt


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What are spot rates?

Spot ratesthe interest rate applicable for a specificperiod starting from today

Also known as zero coupon rates

Spot rate curve constructed from spot rates for variousmaturities

Spot rates are not directly observed in the market

Derived from the normal yield curve by thebootstrapping method


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What are forward rates?

Suppose an investor has a one-year investment horizon

He has 2 alternatives:

Buy a 1-year Treasury Bill

Buy a 6-month Treasury Bill and after it matures in six months,buy another 6-month T-Bill

The investor will be indifferent between the 2 alternatives whenboth alternatives give him the same return over his one yearhorizon

Investor knows the spot rates on the 6-month T-Bill and 1-year T-

Bill

What will be the spot rate for a 6-month T-Bill purchased 6 monthsfrom now?


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Why compute forward rates?

Forward rates implied from current spot rates indicate theinterest rates expected to prevail in the future

An investors strategy will depend on whether his expectations

are different from that of the market

Example An investor wants to invest Rs.50 lakhs for a one-year horizon

He can either invest directly for one year at the one-year spot rate orinvest for six months at the 6-month rate and renew the deposit at theend of 6 months at the rate prevailing then

The six month spot rate is 7% and the one-year spot rate is 6%

This implies a rate of 5% for the six-month period starting 6 monthsfrom now

What will the investor do?


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Computation of forward ratesWhere rf is forward rate, rl = long-term deposit rate, rs=short-termdeposit rate, nl =number of days in

long term, ns=number of days inshort-term and nf=number of daysin forward period

When period is less than 1 year, the general formula is


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Computation of forward ratesWhen period is more than 1 year, the general formula is

(1+rl)nl/12 = (1+rs)ns/12 * (1+f)nf/12

Where rl = rate for long period and nl =number of months in longperiod, rs = rate for short period and ns=number of months in short

period, f =forward rate and nf =number of months in forward period

Period Spot rate

R(0,1) 8.00%

R (0,2) 8.80%

R (0,3) 9.00%

R (0,4) 9.30%

R (0,5) 9.50%


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An examplePeriod Spot rate

R(0,1) 8.00%

R (0,2) 8.80%

R (0,3) 9.00%R (0,4) 9.30%

R (0,5) 9.50%

An investor has a 5-year investmenthorizon. Should he (a) Invest in a 5-yearbond or (b) Invest in a 2 year-bond todayand roll over the maturity proceeds into a3-year bond?

Investment for 5 years starting today will yield (1+.095) 5Investment for 2 years starting today will yield (1+.088)^2Investment for 3 years starting 2 yrs from now will yield (1+f)^(3)Hence f =(( (1+.095)^5)/((1+.088)^2))^(1/3)-1The implied 3-year forward rate starting 2 years from now is 9.97%If the investors view is that the 3-year interest rate 2 years from now will belower than 9.97%, he should go for (a) else go for (b)


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Forward Rate Agreements

A product to hedge against interest ratefluctuations for short periods

Can be used to lock in a rate of interest for aborrowing or investment for a fixed periodstartingn periods from now

Can be used for hedging against expected rise aswell as decline in interest rates


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Borrowers FRA

A company wants to borrow Rs.50 crore three monthsfrom now for a project which will take around 6months. Its current borrowing cost is 9%. The

Company anticipates the central bank to raise interestrates in December. The bankers are quoting a 3/9 FRAat 9.25%-9.75%. How can the Company hedge againstthe rise in interest rates? What will be the effective cost

of borrowing for the Company if the interest rate is10% at the end of three months from today?What ifinterest rate is at 8%?


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Investors FRA A company expects a cash dividend of Rs.50 crore

from its subsidiary three months from now. The CFOdoes not anticipate any requirement for these funds for

a period of 6 months. Six-month bulk deposit rate isaround 8.50% today. The CFO apprehends a decline ininterest rates around December. The bankers arequoting a 3/9 FRA at 8.45%-8.75%. How can the

Company hedge against a decline in interest rates?What will be the effective yield earned on the deposit ifthe interest rate is 8 % at the end of three months fromtoday?What if interest rate is at 9%?

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Lecture 3_InterestRatesForwards.pptx