Money Markets

Reading: Chapter VI

Cuthbertson & Nitzsche:

Money Markets 2

Money Market Instruments• Money market (MMI) instruments are

typically short-term intruments for borrowing and lending.

• Gains from holding MMI: the price paid lies below the price received at maturity.

• Two forms:– Buy security at a discount, i.e. P < FV

‘Dollar Discount’: D = FV – P.– Earn interest, i.e. TV > FV ‘Dollar Interest’:

TV – FV.

Money Markets 3

Caveats

• Securities traded in market have varying maturities.• Changing interest rate environment implies the rate of

return on new issues may differ from the original rate of return on older issues Price of older issues must adjust to compensate.

• Rates quoted may refer to different ‘day count conventions’

• Rates quoted may be on discount or on yield basis Need to find valid basis for comparison, i.e. agreed

upon measures of return, in order to find correct price, given FV and time to maturity, t.

Money Markets 4

Key Variables for Financial Assets

• Price paid

• Maturity value

• Interest (coupon) payments

• Dates money changes hands

• Legal Aspects

• Risks

Money Markets 5

Key co-ordinates of MM Instruments

• Key coordinates:– Amount received– Time elapsed from payment to receipt (time to

maturity)– Amount invested

• From these coordinates a rate of return can be calculated

• Here we ignore risk and legal aspects

Money Markets 6

Rate of Return Conventions

• There exist various rates of return that are quoted MMIs

• They depend on a number of conventions:– Day count convention examples:

• Actual/Actual• Actual/360• 30/360 [Months assumed to have 30 days: Continental]

– Discount (PFV) vs. yield (FVTV)

• Annualised return? Simple annualised return usually quoted.

Money Markets 7

360 vs. 365 Day Year

• Loan type example:

• 360: €1,000,000, 10%, 3 months:

0.1(90/360)1,000,000 = 25,000

• 365: €1,000,000, 10%, 3 months:

0.1(90/365)1,000,000 = 24,657

• Convert 360365: 0.1(365/360) = 0.10139

Money Markets 8

Number of Days to Maturity

• 4.12. 12.05.:– Actual 159 days– 30 day months 4.12.4.05. is 150 days– 4.05.12.05.: 8 days By 30 day month rule: 158 days.

• Implied annualisation factor:– Actual/actual: 159/365– Actual/360: 159/360– 30/360: 158/360

Money Markets 9

Pricing Pure Discount Instruments

• Annualised discount rate:

• Price:

• Dollar Discount:

a = days in year & m = days to maturityN.B.: d is expressed in % terms

FV P ad

FV m

1m

P FV da

mD FV d

a

Money Markets 10

Example Pure Discount Instrument

• 91-day UK T-Bill actual/actual, FV = £1m, P = 950,000

• Discount rate?d = 0.2005= [(1,000,000-950,000)/1,000,000](365/91)

• ‘Sterling Discount?D = £50,000

• Yield?y = 0.2111

Money Markets 11

From Discount to Yield

• Replace FV in the denominator with P:

• or

• y > d• The greater is y or d, the greater is (y-d)

FV P ay

P m

FVy d

P

Money Markets 12

Example discount Instrument

• UK Bank Acceptance for £1m, 87 days to maturity, P such that 12% discount.

• Sterling Discount?

• Price?

871,000,000 0.12 28,602.74365D

Money Markets 13

Yield Quoted Instruments

• Annualised Yield:

• Price:

• Terminal Value:

TV P ay

P m

1

TVP

my

a

1m

TV P ya

Money Markets 14

Notice the equivalent Functional Form

TV P ay

P m

FV P ad

FV m

Money Markets 15

Example: Yield Instrument

• Issue: £1m CD @ 12.5% for 120 days• Resale in secondary Market 58 days later to

yield 11%• Price?

Check results…

621,000,000 1 0.125 1,041,095.89365FV

21,041,095.89 1,021,999.99

621 0.11 365ndaryMktP

Money Markets 16

Comparison: US Money & Bond Rates

• Money Market Price: P = 95, FV = 100, m = 91

• Bond Market Price: Pb = 95, FV = 100, m = 91

• Money Market Discount Rate:

• Bond Market Discount Rate:

• Money Market Yield:

• Bond Market Yield:

• Money Market ‘Bond Yield Equivalent’:

100 360100 19.78%

100 91

Pd

* 100 365100 20.05%

100 91bPd

100 36020.82%

91

Py

P

100 365100 21.11%

91b

b

PY

P

36521.11%

360BY y

Money Markets 17

Example: US T-Bill

• P = 97.912 FV = 100 m = 182 act./360• d?

100 97.912 3600.0413

100 182d

Money Markets 18

Example: US CD

• $1m 90 days 7% yield act./360• TV?

901,000,000 1 0.07 1,017,500

360TV

Money Markets 19

Example: US CD

• Actual/360• Original issue: $5m to yield 7.25%, 60 days• Sold after 39 days to yield 7%• At what price did the CD trade?• Find discounted present value of TV:

2

601 0.0725 360 5,000,000211 0.07 360

ndaryP

Money Markets 20

Comparing Rates

1. Convert to Prices

2. Calculate benchmark rate (often compound)• US T-Bill, 90 days, d = 0.1, FV = $100 ,

act./360

• PT= 100-10(90/360)=97.5, D = 2.5

• Simple Annual: [(100/97.5)-1](365/90) = 0.104• Compound return: [(100/97.5)365/90-1] = 0.108

Money Markets 21

Comparing Rates (continued)

• Eurodollar, 90 days, y = 0.1, act./360

• TV = 97.5[1+0.1(90/360)] = 99.94

• Simple Annual:

[(99.94/97.5)-1](365/90) = 0.1015

• Compound:

(99.94/97.5)365/90-1 = 0.1054