Analyst Dojo

CFA Level I Economics formulas

Profit and cost rules for each market structure, concentration measures, the fiscal multipliers, trade policy effects and exchange rate arithmetic, including cross rates and forward points.

61 formulas from the Economics lessons (6–9% of the exam), 27 to memorize. Each says how deeply to learn it and opens to a quick worked example with the keystrokes for the TI BA II Plus and the HP 12C.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.

Module 1 The Firm and Market Structures

Breakeven and shutdown points

Profit-maximizing output Memorize
MR=MC(with MC rising)MR = MC \quad (\text{with } MC \text{ rising})
Quick example

Demand is P=100−5QP = 100 - 5Q, so MR=100−10QMR = 100 - 10Q. With MC=20MC = 20: Q=(100−20)÷10=Q = (100 - 20) \div 10 = 8.

On your calculator
  1. 100−20=÷10= 8
  1. 100ENTER20−10÷ 8

ENTER enter (on the HP, puts the number on the stack)

Economic profit Use it
Economic profit=TR−(explicit costs+implicit costs)\text{Economic profit} = TR - (\text{explicit costs} + \text{implicit costs})
Quick example

Revenue 500, accounting costs 380, and 600 of owners' capital that could earn 12% elsewhere (72). 500 − 380 − 72 = 48.

On your calculator
  1. 600×0.12=STO1
  2. 500−380−RCL1= 48

STO store · RCL recall a stored number

  1. 500ENTER380−600ENTER0.12×− 48

ENTER enter (on the HP, puts the number on the stack)

Breakeven point Memorize
TR=TC  ⇔  P=ATCTR = TC \;\Leftrightarrow\; P = ATC
Quick example

Fixed cost 60,000, variable cost 8 a unit, 10,000 units. ATC=60,000÷10,000+8=ATC = 60{,}000 \div 10{,}000 + 8 = 14, so the breakeven price is 14.

On your calculator
  1. 60000÷10000+8= 14
  1. 60000ENTER10000÷8+ 14

ENTER enter (on the HP, puts the number on the stack)

Shutdown rule (short run) Memorize
TR<TVC  ⇔  P<AVC  ⇒  shut downTR < TVC \;\Leftrightarrow\; P < AVC \;\Rightarrow\; \text{shut down}
Quick example

Price 7 against average variable cost 8: each unit loses 1 before any fixed cost. Producing loses more than the fixed cost alone, so shut down.

Short-run profit of a price taker Use it
π=(P−AVC) Q−TFC\pi = (P - AVC)\,Q - TFC
Quick example

Price 11, variable cost 8, 10,000 units, fixed cost 60,000. (11 − 8) × 10,000 − 60,000 = −30,000, a loss smaller than the 60,000 lost by shutting down.

On your calculator
  1. 11−8=×10000−60000= −30000
  1. 11ENTER8−10000×60000− −30000

ENTER enter (on the HP, puts the number on the stack)

Economies and diseconomies of scale

Returns to scale Memorize
%Δoutput%Δinputs  {>1increasing (economies)=1constant<1decreasing (diseconomies)\dfrac{\%\Delta \text{output}}{\%\Delta \text{inputs}} \;\begin{cases} > 1 & \text{increasing (economies)} \\ = 1 & \text{constant} \\ < 1 & \text{decreasing (diseconomies)} \end{cases}
Quick example

All inputs rise 10% and output rises 6%. 6 ÷ 10 = 0.6, below 1: decreasing returns, so diseconomies of scale.

On your calculator
  1. 6÷10= 0.6
  1. 6ENTER10÷ 0.6

ENTER enter (on the HP, puts the number on the stack)

Change in cost per unit from scaling up Use it
gu=1+gin1+gout−1(input prices unchanged)g_u = \dfrac{1 + g_{in}}{1 + g_{out}} - 1 \quad (\text{input prices unchanged})
Quick example

Inputs +10% and output +6%. 1.10 ÷ 1.06 − 1 = +3.8%: cost per unit rises.

On your calculator
  1. 1.1÷1.06−1= 0.0377
  1. 1.1ENTER1.06÷1− 0.0377

ENTER enter (on the HP, puts the number on the stack)

Monopolistic competition: price, output and the long run

Marginal revenue with linear demand Use it
P=a−bQ  ⇒  MR=a−2bQP = a - bQ \;\Rightarrow\; MR = a - 2bQ
Quick example

Demand P=48−2QP = 48 - 2Q gives MR=48−4QMR = 48 - 4Q. At Q=5Q = 5, MR=48−20=MR = 48 - 20 = 28, below the price of 38.

On your calculator
  1. 4×5=+|-+48= 28

+|- change sign

  1. 4ENTER5×CHS48+ 28

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Profit-maximizing output and price Use it
MR=MC  ⇒  Q∗=a−MC2b,P∗=a−bQ∗MR = MC \;\Rightarrow\; Q^* = \dfrac{a - MC}{2b}, \qquad P^* = a - bQ^*
Quick example

Demand P=30−0.5QP = 30 - 0.5Q, MC=10MC = 10. Q∗=(30−10)÷(2×0.5)=Q^* = (30 - 10) \div (2 \times 0.5) = 20, then P∗=30−0.5×20=P^* = 30 - 0.5 \times 20 = 20.

On your calculator
  1. 30−10=÷1= 20 (2 × 0.5 = 1)
  2. 0.5×20=+|-+30= 20

+|- change sign

  1. 30ENTER10−1÷ 20 (2 × 0.5 = 1)
  2. 0.5ENTER20×CHS30+ 20

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Economic profit per period Use it
π=(P−ATC) Q\pi = (P - ATC)\,Q
Quick example

Price 20, ATC 16, output 20 hundred cases. (20 − 16) × 20 = 80 hundred, or USD 8,000.

On your calculator
  1. 20−16=×20= 80
  1. 20ENTER16−20× 80

ENTER enter (on the HP, puts the number on the stack)

Long-run equilibrium under monopolistic competition Memorize
P=ATC,P>MC,Q<Qmin⁡ATCP = ATC, \quad P > MC, \quad Q < Q_{\min ATC}
Quick example

Zero economic profit, price above marginal cost, and output below the cost-minimizing level (excess capacity).

Oligopoly pricing: kinked demand, Cournot, Nash and Stackelberg

Cournot equilibrium with n identical firms Use it
Q=nn+1⋅a−MCb,P=a−bQQ = \dfrac{n}{n + 1} \cdot \dfrac{a - MC}{b}, \qquad P = a - bQ
Quick example

Demand P=100−QP = 100 - Q, MC=10MC = 10, two firms. Q=23×90=Q = \tfrac{2}{3} \times 90 = 60 and P=100−60=P = 100 - 60 = 40.

On your calculator
  1. 100−10=÷1×2÷3= 60
  1. 100ENTER10−1÷2×2ENTER1+÷ 60

ENTER enter (on the HP, puts the number on the stack)

Price and output ordering Memorize
Pmonopoly>PCournot>Pcompetition=MC,Qmonopoly<QCournot<QcompetitionP_{monopoly} > P_{Cournot} > P_{competition} = MC, \qquad Q_{monopoly} < Q_{Cournot} < Q_{competition}
Quick example

Demand P=100−QP = 100 - Q, MC=10MC = 10. Monopoly: 45 units at 55. Cournot duopoly: 60 at 40. Perfect competition: 90 at 10.

Concentration ratio and Herfindahl-Hirschman index

N-firm concentration ratio Memorize
CRN=s1+s2+⋯+sNCR_N = s_1 + s_2 + \cdots + s_N
Quick example

Shares of the top four firms are 30%, 22%, 18% and 12%. 30 + 22 + 18 + 12 = 82%.

On your calculator
  1. 30+22+18+12= 82
  1. 30ENTER22+18+12+ 82

ENTER enter (on the HP, puts the number on the stack)

Herfindahl-Hirschman index Memorize
HHIN=s12+s22+⋯+sN2(shares as decimals)HHI_N = s_1^2 + s_2^2 + \cdots + s_N^2 \quad (\text{shares as decimals})
Quick example

Top four shares 38%, 27%, 21%, 14%. 0.1444 + 0.0729 + 0.0441 + 0.0196 = 0.281.

On your calculator
  1. 0.38x²+0.27x²+0.21x²+0.14x²= 0.281

x² square

  1. 0.38ENTER×0.27ENTER×+0.21ENTER×+0.14ENTER×+ 0.281, ENTER then × squares

ENTER enter (on the HP, puts the number on the stack)

Equivalent number of equal-sized firms Memorize
HHI=1M  ⇒  M=1HHIHHI = \dfrac{1}{M} \;\Rightarrow\; M = \dfrac{1}{HHI}
Quick example

An HHI of 0.125 is like 8 equal-sized firms (1 ÷ 0.125).

On your calculator
  1. 0.1251/x 8

1/x reciprocal

  1. 0.1251/x 8

1/x reciprocal

Rise in the all-firm HHI from a merger Use it
ΔHHI=2 s1 s2\Delta HHI = 2\,s_1\,s_2
Quick example

Two firms with 25% and 10% shares merge. 2 × 0.25 × 0.10 = 0.05.

On your calculator
  1. 2×0.25×0.1= 0.05
  1. 2ENTER0.25×0.1× 0.05

ENTER enter (on the HP, puts the number on the stack)

Module 2 Understanding Business Cycles

Employment, capital spending, inventories, housing and trade over the cycle

Inventory–sales ratio Use it
R=inventorysalesR = \dfrac{\text{inventory}}{\text{sales}}
Quick example

A retailer holds USD 49 million of stock and monthly sales fall from USD 35 million to USD 28 million. The ratio moves from 1.40 to 49 ÷ 28 = 1.75.

On your calculator
  1. 49÷28= 1.75
  1. 49ENTER28÷ 1.75

ENTER enter (on the HP, puts the number on the stack)

Leading, coincident and lagging economic indicators

Diffusion index Use it
DI=U+0.5FN×100DI = \dfrac{U + 0.5F}{N} \times 100
Quick example

Eight components: 5 rise by more than 0.05%, 1 is within ±0.05%, 2 fall. (5 + 0.5) ÷ 8 × 100 = 68.75, a broad upward move.

On your calculator
  1. 5+0.5=÷8×100= 68.75
  1. 5ENTER0.5+8÷100× 68.75

ENTER enter (on the HP, puts the number on the stack)

Module 3 Fiscal Policy

Fiscal vs monetary policy and what fiscal policy is for

Budget deficit Use it
D=G+B−TD = G + B - T
Quick example

Spending on goods and services (with debt interest) is 330, transfers are 150 and tax revenue is 400. D = 330 + 150 − 400 = 80, a deficit of 80.

On your calculator
  1. 330+150−400= 80
  1. 330ENTER150+400− 80

ENTER enter (on the HP, puts the number on the stack)

Does the size of national debt matter?

Next year's debt-to-GDP ratio Use it
d1=d0×1+r1+gd_1 = d_0 \times \dfrac{1 + r}{1 + g}
Quick example

Debt is 60% of GDP, the real interest rate is 1.5% and real growth is 3.5%. 60 × 1.015 ÷ 1.035 = 58.8%: growth above the interest rate pulls the ratio down.

On your calculator
  1. 60×1.015÷1.035= 58.84
  1. 60ENTER1.015×1.035÷ 58.84

ENTER enter (on the HP, puts the number on the stack)

Fiscal policy tools and the fiscal multiplier

Disposable income Use it
YD=(1−t) YY_D = (1 - t)\,Y
Quick example

Income is 600 and the net tax rate is 35%. Disposable income = 0.65 × 600 = 390.

On your calculator
  1. 1−0.35=×600= 390
  1. 1ENTER0.35−600× 390

ENTER enter (on the HP, puts the number on the stack)

Fiscal multiplier Memorize
k=11−MPC (1−t)k = \dfrac{1}{1 - MPC\,(1 - t)}
Quick example

MPC 0.65 and net tax rate 45%. k = 1 ÷ [1 − 0.65 × 0.55] = 1 ÷ 0.6425 = 1.56. Without taxes it would be 1 ÷ 0.35 = 2.86.

On your calculator
  1. 1−0.45=×0.65=+|-+1=1/x 1.5564

+|- change sign · 1/x reciprocal

  1. 1ENTER0.45−0.65×CHS1+1/x 1.5564

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · 1/x reciprocal

Change in output Use it
ΔY=k×ΔG\Delta Y = k \times \Delta G
Quick example

With k = 1 ÷ 0.6425 = 1.56, government spending of GBP 12 billion raises output by 12 ÷ 0.6425 = GBP 18.7 billion, given spare capacity.

On your calculator
  1. 12÷0.6425= 18.68
  1. 12ENTER0.6425÷ 18.68

ENTER enter (on the HP, puts the number on the stack)

Balanced budget multiplier Memorize
kBB=1k_{BB} = 1
Quick example

Spending and taxes both rise by GBP 50 billion. Output rises by GBP 50 billion, a multiplier of 1, however large the ordinary multiplier is.

Is fiscal policy expansionary? Structural deficits and policy lags

Change in the deficit Use it
ΔD=ΔG+ΔB−ΔT\Delta D = \Delta G + \Delta B - \Delta T
Quick example

Spending on goods and services rises by 1% of GDP, transfers are unchanged, taxes rise by 3% of GDP. ΔD = 1 + 0 − 3 = −2% of GDP: the deficit shrinks, so policy is contractionary.

On your calculator
  1. 1−3= −2, contractionary
  1. 1ENTER3− −2, contractionary

ENTER enter (on the HP, puts the number on the stack)

Structural budget deficit Use it
S=A−CS = A - C
Quick example

The actual deficit is 4.5% of GDP, of which 1.2% of GDP is cyclical. S = 4.5 − 1.2 = 3.3% of GDP.

On your calculator
  1. 4.5−1.2= 3.3
  1. 4.5ENTER1.2− 3.3

ENTER enter (on the HP, puts the number on the stack)

Inflation-adjusted deficit Know the idea
Dreal=D−π×debtD_{real} = D - \pi \times \text{debt}
Quick example

Debt is 800, inflation is 3% and the deficit is 50. Inflation erodes 0.03 × 800 = 24 of the debt, so the real deficit is 50 − 24 = 26.

On your calculator
  1. 800×0.03=+|-+50= 26

+|- change sign

  1. 800ENTER0.03×CHS50+ 26

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Module 4 Monetary Policy

Monetary policy tools and the transmission mechanism

Bank lending rate Use it
L=P+sL = P + s
Quick example

The policy rate (and so the base rate) is 2.00%. A bank lends to a mid-sized firm at base plus 2.5%. L = 2.00 + 2.5 = 4.50%. If the policy rate rises to 2.50%, the loan rate becomes 5.00%.

On your calculator
  1. 2+2.5= 4.5
  1. 2ENTER2.5+ 4.5

ENTER enter (on the HP, puts the number on the stack)

Neutral rate, expansionary vs contractionary policy and the limits of monetary policy

Neutral rate of interest Memorize
N=g+πeN = g + \pi^{e}
Quick example

Real trend growth is 1.6% and the inflation target is 2.0%. N = 1.6 + 2.0 = 3.6%. A policy rate above 3.6% is contractionary; below it, expansionary.

On your calculator
  1. 1.6+2= 3.6
  1. 1.6ENTER2+ 3.6

ENTER enter (on the HP, puts the number on the stack)

Policy stance gap Use it
G=P−NG = P - N
Quick example

The neutral rate is 3.9% and the policy rate is 4.35%. G = 4.35 − 3.9 = +0.45 points: positive, so policy is contractionary.

On your calculator
  1. 4.35−3.9= 0.45
  1. 4.35ENTER3.9− 0.45

ENTER enter (on the HP, puts the number on the stack)

Module 6 International Trade

Benefits and costs of international trade

Opportunity cost of a good Use it
OCX=output of the other good, Youtput of this good, XOC_X = \dfrac{\text{output of the other good, } Y}{\text{output of this good, } X}
Quick example

In a worker-day a country makes 8 shirts or 4 phones. A phone costs 8 ÷ 4 = 2 shirts; a shirt costs 4 ÷ 8 = 0.5 phone.

On your calculator
  1. 8÷4= 2 shirts per phone
  1. 8ENTER4÷ 2 shirts per phone

ENTER enter (on the HP, puts the number on the stack)

Range of mutually beneficial prices Use it
OCexporter<Ptrade<OCimporterOC_{\text{exporter}} < P_{\text{trade}} < OC_{\text{importer}}
Quick example

A phone costs 2 shirts in X and 1 shirt in Y. Any price strictly between 1 and 2 shirts per phone leaves both countries better off; 1.5 works.

Tariffs, quotas, export subsidies and their welfare effects

Domestic price with a tariff Memorize
Pt=P∗+tP_t = P^{*} + t
Quick example

World price 25, tariff 3 per unit, small country: the domestic price is 28.

On your calculator
  1. 25+3= 28
  1. 25ENTER3+ 28

ENTER enter (on the HP, puts the number on the stack)

Consumer surplus lost (A + B + C + D) Use it
ΔCS=t Qd,after+12 t ΔQd\Delta CS = t\,Q_{d,\text{after}} + \tfrac{1}{2}\,t\,\Delta Q_d
Quick example

Tariff 4. Consumption falls by 50 to 360 units. Lost surplus = 4 × 360 + ½ × 4 × 50 = 1,540.

On your calculator
  1. 50÷2+360=×4= 1540
  1. 50ENTER2÷360+4× 1540

ENTER enter (on the HP, puts the number on the stack)

Producer surplus gained (A) Use it
ΔPS=t Qs,before+12 t ΔQs\Delta PS = t\,Q_{s,\text{before}} + \tfrac{1}{2}\,t\,\Delta Q_s
Quick example

Tariff 4. Output rises by 20 from 110 units. Gain = 4 × 110 + ½ × 4 × 20 = 480.

On your calculator
  1. 20÷2+110=×4= 480
  1. 20ENTER2÷110+4× 480

ENTER enter (on the HP, puts the number on the stack)

Tariff revenue (C) Use it
R=t×(imports after the tariff)R = t \times (\text{imports after the tariff})
Quick example

Tariff 4. Imports fall from 300 to 230 units. Revenue = 4 × 230 = 920.

On your calculator
  1. 230×4= 920
  1. 230ENTER4× 920

ENTER enter (on the HP, puts the number on the stack)

Deadweight loss of a tariff (B + D) Memorize
DWL=12 t ΔQs+12 t ΔQdDWL = \tfrac{1}{2}\,t\,\Delta Q_s + \tfrac{1}{2}\,t\,\Delta Q_d
Quick example

Tariff 4, output up 20, consumption down 50. ½ × 4 × 20 + ½ × 4 × 50 = 40 + 100 = 140. Check: 1,540 − 480 − 920 = 140.

On your calculator
  1. 20+50=×4÷2= 140
  1. 20ENTER50+4×2÷ 140

ENTER enter (on the HP, puts the number on the stack)

National loss from a quota (rent to foreigners) Use it
Loss=B+C+D\text{Loss} = B + C + D
Quick example

Same figures: deadweight loss 140 plus rent 920 = 1,060. With auctioned licenses the loss is only 140.

On your calculator
  1. 140+920= 1060
  1. 140ENTER920+ 1060

ENTER enter (on the HP, puts the number on the stack)

Trading blocs: free trade areas, customs unions, common markets and economic unions

Price after an external tariff Use it
Pt=P (1+t)P_t = P\,(1 + t)
Quick example

Outsider's good costs 66 and the bloc's external tariff is 20%. 66 × 1.20 = 79.20, against 75 from a member, so buyers switch to the member (90 with the tariff before the union): diversion.

On your calculator
  1. 66×1.2= 79.2
  1. 66ENTER1.2× 79.2

ENTER enter (on the HP, puts the number on the stack)

Net welfare effect of a bloc Know the idea
N=Uc s−Ud eN = U_c\,s - U_d\,e
Quick example

3,000 units of creation saving 5 each, 2,000 units of diversion costing 4 more each. 15,000 − 8,000 = +7,000: creation outweighs diversion.

On your calculator
  1. 2000×4=STO1
  2. 3000×5−RCL1= 7000

STO store · RCL recall a stored number

  1. 3000ENTER5×2000ENTER4×− 7000

ENTER enter (on the HP, puts the number on the stack)

Module 7 Capital Flows and the FX Market

Exchange rate quotes and percentage change in a currency

Percentage change in the base currency Memorize
%ΔB=S1S0−1\%\Delta B = \frac{S_1}{S_0} - 1
Quick example

The EUR/GBP quote (euros per pound) rises from 1.1500 to 1.1960. The pound, the base currency, has changed by 1.1960 ÷ 1.1500 − 1 = +4.00%.

On your calculator
  1. 1.196÷1.15−1= 0.04
  1. 1.196ENTER1.15÷1− 0.04

ENTER enter (on the HP, puts the number on the stack)

Percentage change in the price currency Memorize
%ΔA=S0S1−1\%\Delta A = \frac{S_0}{S_1} - 1
Quick example

Same move, EUR/GBP from 1.1500 to 1.1960. The euro, the price currency, has changed by 1.1500 ÷ 1.1960 − 1 = −3.85%.

On your calculator
  1. 1.15÷1.196−1= −0.0385
  1. 1.15ENTER1.196÷1− −0.0385

ENTER enter (on the HP, puts the number on the stack)

Inverting a two-sided quote Memorize
bidB/A=1offerA/B,offerB/A=1bidA/B\text{bid}_{B/A} = \frac{1}{\text{offer}_{A/B}}, \quad \text{offer}_{B/A} = \frac{1}{\text{bid}_{A/B}}
Quick example

USD/CAD 1.3640 – 1.3646 becomes CAD/USD (1 ÷ 1.3646) – (1 ÷ 1.3640) = 0.7328 – 0.7331.

On your calculator
  1. 1.36461/x 0.7328
  2. 1.3641/x 0.7331

1/x reciprocal

  1. 1.36461/x 0.7328
  2. 1.3641/x 0.7331

1/x reciprocal

Nominal vs real exchange rates

Real exchange rate Memorize
Rd/f=Sd/f×PfPdR_{d/f} = S_{d/f} \times \frac{P_f}{P_d}
Quick example

A Mexican buyer faces MXN/USD 18.00, a US price index of 110 and a Mexican index of 120. R = 18.00 × 110 ÷ 120 = 16.50.

On your calculator
  1. 18×110÷120= 16.5
  1. 18ENTER110×120÷ 16.5

ENTER enter (on the HP, puts the number on the stack)

Change in the real exchange rate (exact) Memorize
%ΔR=(1+%ΔS)(1+%ΔPf)1+%ΔPd−1\%\Delta R = \frac{(1 + \%\Delta S)(1 + \%\Delta P_f)}{1 + \%\Delta P_d} - 1
Quick example

The nominal d/f rate rises 2%, foreign prices 5% and domestic prices 3%. 1.02 × 1.05 ÷ 1.03 − 1 = +3.98%.

On your calculator
  1. 1.02×1.05÷1.03−1= 0.0398
  1. 1.02ENTER1.05×1.03÷1− 0.0398

ENTER enter (on the HP, puts the number on the stack)

Change in the real exchange rate (approximate) Use it
%ΔR≈%ΔS+%ΔPf−%ΔPd\%\Delta R \approx \%\Delta S + \%\Delta P_f - \%\Delta P_d
Quick example

Same inputs: 2% + 5% − 3% = 4%, close to the exact 3.98%.

Exchange rate regimes and their effects on trade and capital flows

Trade balance identity Memorize
X−M=(S−I)+(T−G)X - M = (S - I) + (T - G)
Quick example

Private saving is 15% of GDP, investment 19% and the government balance −1%. X − M = (15 − 19) + (−1) = −5% of GDP, a deficit financed by capital inflows.

On your calculator
  1. 15−19+1+|-= −5

+|- change sign

  1. 15ENTER19−1CHS+ −5

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Module 8 Exchange Rate Calculations

Currency cross-rates and triangular arbitrage

Cross-rate by cancelling the common currency Memorize
AB=AC×CB\frac{A}{B} = \frac{A}{C} \times \frac{C}{B}
Quick example

SEK/USD is 9.60 and USD/NZD is 0.5900. The common currency (USD) cancels: SEK/NZD = 9.60 × 0.5900 = 5.664.

On your calculator
  1. 9.6×0.59= 5.664
  1. 9.6ENTER0.59× 5.664

ENTER enter (on the HP, puts the number on the stack)

Inverting a quote Memorize
CB=1B/C\frac{C}{B} = \frac{1}{B/C}
Quick example

CAD/USD is 1.3600, but the cross needs USD/CAD: 1 ÷ 1.3600 = 0.7353.

On your calculator
  1. 1.361/x 0.7353

1/x reciprocal

  1. 1.361/x 0.7353

1/x reciprocal

Cross-rate by dividing two quotes Memorize
AB=A/CB/C=C/BC/A\frac{A}{B} = \frac{A/C}{B/C} = \frac{C/B}{C/A}
Quick example

SEK/USD is 9.60 and CAD/USD is 1.3600 (same base, USD). SEK/CAD = 9.60 ÷ 1.3600 = 7.0588.

On your calculator
  1. 9.6÷1.36= 7.0588
  1. 9.6ENTER1.36÷ 7.0588

ENTER enter (on the HP, puts the number on the stack)

Percentage change in a cross-rate Use it
%ΔB=X1X0−1\%\Delta B = \frac{X_1}{X_0} - 1
Quick example

The JPY/GBP cross moves from 190.20 to 193.05. The pound (the base currency) changed by 193.05 ÷ 190.20 − 1 = +1.50%.

On your calculator
  1. 193.05÷190.2−1= 0.015
  1. 193.05ENTER190.2÷1− 0.015

ENTER enter (on the HP, puts the number on the stack)

Forward points, forward premiums and discounts

Forward rate from forward points Memorize
F=S+points10,000(yen pairs: points100)F = S + \frac{\text{points}}{10{,}000} \qquad \left(\text{yen pairs: } \frac{\text{points}}{100}\right)
Quick example

CHF/EUR spot is 0.9400 and the 1-year points are +36.0. F = 0.9400 + 36.0 ÷ 10,000 = 0.9436.

On your calculator
  1. 36÷10000+0.94= 0.9436
  1. 36ENTER10000÷0.94+ 0.9436

ENTER enter (on the HP, puts the number on the stack)

Forward points from the two rates Use it
points=(F−S)×10,000\text{points} = (F - S) \times 10{,}000
Quick example

Spot 0.7350 and forward 0.7392. Points = (0.7392 − 0.7350) × 10,000 = +42.0.

On your calculator
  1. 0.7392−0.735=×10000= 42
  1. 0.7392ENTER0.735−10000× 42

ENTER enter (on the HP, puts the number on the stack)

Forward premium (discount) in percent Memorize
premium (discount)=FS−1\text{premium (discount)} = \frac{F}{S} - 1
Quick example

Spot 0.7350 and forward 0.7392. The base currency is at a premium of 0.7392 ÷ 0.7350 − 1 = +0.57%.

On your calculator
  1. 0.7392÷0.735−1= 0.0057
  1. 0.7392ENTER0.735÷1− 0.0057

ENTER enter (on the HP, puts the number on the stack)

Forward rate from a percentage Use it
F=S×(1+premium)F = S \times (1 + \text{premium})
Quick example

Spot 0.9400 and a forward premium of 0.40%. F = 0.9400 × 1.004 = 0.94376.

On your calculator
  1. 0.94×1.004= 0.94376
  1. 0.94ENTER1.004× 0.94376

ENTER enter (on the HP, puts the number on the stack)

Covered interest rate parity: forward rates from interest rates

No-arbitrage condition Use it
1+rB τ=S×(1+rA τ)×1F1 + r_B\,\tau = S \times (1 + r_A\,\tau) \times \frac{1}{F}
Quick example

CHF/EUR spot 0.9400, 180-day forward 0.93076, CHF rate 1.5%, EUR rate 3.5%. Deposit EUR: 1 + 0.035 × 0.5 = 1.0175. Swap route: 0.9400 × 1.0075 ÷ 0.93076 = 1.0175. Equal.

On your calculator
  1. 0.94×1.0075÷0.93076= 1.0175
  1. 0.94ENTER1.0075×0.93076÷ 1.0175

ENTER enter (on the HP, puts the number on the stack)

Covered interest rate parity: the forward rate Memorize
FA/B=SA/B×1+rA τ1+rB τF_{A/B} = S_{A/B} \times \frac{1 + r_A\,\tau}{1 + r_B\,\tau}
Quick example

CHF/EUR spot 0.9400, CHF rate 1.5%, EUR rate 3.5%, 180 days. F = 0.9400 × 1.0075 ÷ 1.0175 = 0.93076. The EUR (the higher-rate currency) trades at a forward discount.

On your calculator
  1. 0.94×(0.015×180÷360+1)÷(0.035×180÷360+1)= 0.93076
  1. 0.94ENTER0.015ENTER180×360÷1+×0.035ENTER180×360÷1+÷ 0.93076

ENTER enter (on the HP, puts the number on the stack)

Day-count fraction Memorize
τ=days360\tau = \frac{\text{days}}{360}
Quick example

A 270-day forward has τ = 270 ÷ 360 = 0.75, so a 5% annual rate earns 5% × 0.75 = 3.75%.

On your calculator
  1. 270÷360= 0.75
  1. 270ENTER360÷ 0.75

ENTER enter (on the HP, puts the number on the stack)

Forward points from the interest rates Use it
F−S=S×(rA−rB) τ1+rB τF - S = S \times \frac{(r_A - r_B)\,\tau}{1 + r_B\,\tau}
Quick example

Same CHF/EUR inputs. F − S = 0.9400 × (0.015 − 0.035) × 0.5 ÷ 1.0175 = −0.009238, or about −92.4 points.

On your calculator
  1. 0.94×(0.015−0.035)×0.5÷1.0175= −0.009238
  1. 0.94ENTER0.015ENTER0.035−×0.5×1.0175÷ −0.009238

ENTER enter (on the HP, puts the number on the stack)

Expected change in spot if the forward is the forecast Know the idea
%ΔS=rA−rB1+rB\%\Delta S = \frac{r_A - r_B}{1 + r_B}
Quick example

If A pays 6.0% and B pays 2.0%, treating F as the expected spot implies (0.06 − 0.02) ÷ 1.02 = +3.92% for A/B: B is expected to appreciate. Forwards are poor forecasts in practice.

On your calculator
  1. 0.06−0.02=÷1.02= 0.0392
  1. 0.06ENTER0.02−1.02÷ 0.0392

ENTER enter (on the HP, puts the number on the stack)

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