ACI – THE FINANCIAL MARKETS ASSOCIATION

ACI ? THE FINANCIAL MARKETS ASSOCIATION

EXAMINATION FORMULAE

page number INTEREST RATE.............................................................................2 MONEY MARKET.............................................................................3 FORWARD-FORWARDS & FORWARD RATE AGREEMENTS.................4 FIXED INCOME................................................................................5 FOREIGN EXCHANGE.....................................................................7 OPTIONS.......................................................................................8

In all the formulae:

? interest rates, yields, coupon rates and rates of discount are expressed as a decimal, eg 8.53% will be expressed as 0.0853

? `annual basis' is the number of days in a year assumed under the appropriate rate convention

? `term' is the number of days from settlement to maturity of the instrument in question

? `day count' is the number of days from settlement to maturity of the instrument in question.

INTEREST RATE CONVERSIONS

Converting between bond basis and money market basis (Act/360)

ratebond basis

= ratemoney market basis

365 360

ratemoney market basis

= ratebond basis

360 365

Converting between annually and semi-annually compounding frequencies

rate annually-compounded

= 1 +

rate semi-annually compounded 2

2

-1

( ) rate semi-annually compounded = 1 + rate annually compounded - 1 2

The formulae for converting between annually and semi-annually compounded rate apply only to rates quoted on a bond basis, not a money market basis.

2

Certificates of deposit

MONEY MARKET

proceeds at maturity = face value ( 1 + coupon x term ) annual basis

secondary market proceeds = proceeds at maturity 1 + yield x day count annual basis

Discount-paying instruments quoted as a true yield

secondary market proceeds =

face value

1 + yield x day count

annual basis

Discount-paying instruments quoted as a rate of discount

discount amount = face value rate of discount x day count annual basis

secondary market proceeds = face value 1- rate of discount x day count

annual basis

true yield =

rate of discount

1- rate of discount x day count

annual basis

Forward price of sell/buy-back

forward price = (repurchase price - accrued interest on collateral at termination)100

nominal price of collateral

3

FORWARD-FORWARDS & FORWARD RATE AGREEMENTS

forward - forward rate =

1 +

interest

ratelong period x day count long period annual basis

- 1

annual basis

1 +

interest

rate short period x day count annual basis

short

period

day count forward-forward period

(FRA rate - settlement rate) x d ay count

FRA settlement amount = notional principal amount

annual basis

1 + settlement rate x day count

annual basis

4

FIXED INCOME

Clean and dirty price of bond with annual coupons on coupon date

price =

100

coupon yield

1 -

(1 +

1

) yield remaining coupons

+

(1 +

1

) yield remaining coupons

Dirty price of bond with annual coupons

dirty price =

( ) ( ) ( ) first cashflow days to next coupon

1 + yield annual basis

+

second cashflow

1

+

yield

1+

days to next coupon annual basis

+L+

nth cashflow

1+

yield

(n-1)+ days to next coupon

annual basis

Duration at issue or on a coupon date

Macaulay Duration =

(present value of first coupon amount x time to first coupon) +

(present value of second coupon amount x time to second coupon) + ...

+(present value of (last coupon amount + nominal amount ) x time to last coupon)

net present value of bond

Modified Duration =

Macaulay Duration

1 +

yield compounding frequency

5

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