Money Markets Reading: Chapter VI Cuthbertson & Nitzsche:
Money Markets2 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 Markets3 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 Markets4 Key Variables for Financial Assets Price paid Maturity value Interest (coupon) payments Dates money changes hands Legal Aspects Risks
Money Markets5 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 Markets6 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 (P FV) vs. yield (FV TV) Annualised return? Simple annualised return usually quoted.
Money Markets7 360 vs. 365 Day Year Loan type example: 360: €1,000,000, 10%, 3 months: 0.1(90/360)1,000,000 = 25, : €1,000,000, 10%, 3 months: 0.1(90/365)1,000,000 = 24,657 Convert 360 365: 0.1(365/360) =
Money Markets8 Number of Days to Maturity : –Actual 159 days –30 day months is 150 days –4.05. : 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 Markets9 Pricing Pure Discount Instruments Annualised discount rate: Price: Dollar Discount: a = days in year & m = days to maturity N.B.: d is expressed in % terms
Money Markets10 Example Pure Discount Instrument 91-day UK T-Bill actual/actual, FV = £1m, P = 950,000 Discount rate? d = = [(1,000, ,000)/1,000,000](365/91) ‘Sterling Discount? D = £50,000 Yield? y =
Money Markets11 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)
Money Markets12 Example discount Instrument UK Bank Acceptance for £1m, 87 days to maturity, P such that 12% discount. Sterling Discount? Price?
Money Markets13 Yield Quoted Instruments Annualised Yield: Price: Terminal Value:
Money Markets14 Notice the equivalent Functional Form
Money Markets15 Example: Yield Instrument Issue: £1m 12.5% for 120 days Resale in secondary Market 58 days later to yield 11% Price? Check results…
Money Markets16 Comparison: US Money & Bond Rates Money Market Price: P = 95, FV = 100, m = 91 Bond Market Price: P b = 95, FV = 100, m = 91 Money Market Discount Rate: Bond Market Discount Rate: Money Market Yield: Bond Market Yield: Money Market ‘Bond Yield Equivalent’:
Money Markets17 Example: US T-Bill P = FV = 100 m = 182act./360 d?
Money Markets18 Example: US CD $1m90 days7% yieldact./360 TV?
Money Markets19 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:
Money Markets20 Comparing Rates 1.Convert to Prices 2.Calculate benchmark rate (often compound) US T-Bill, 90 days, d = 0.1, FV = $100, act./360 P T = (90/360)=97.5, D = 2.5 Simple Annual: [(100/97.5)-1](365/90) = Compound return: [(100/97.5) 365/90 -1] = 0.108
Money Markets21 Comparing Rates (continued) Eurodollar, 90 days, y = 0.1, act./360 TV = 97.5[1+0.1(90/360)] = Simple Annual: [(99.94/97.5)-1](365/90) = Compound: (99.94/97.5) 365/90 -1 =