Economics (Formulas)

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Last updated 2:04 AM on 10/2/26
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6 Terms

1
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Forward rate parity


<p></p>
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Mark-to-Market Value of a Forward Contract

You are always in a position to make the LEAST spread. Pay attention to whether you are long or short a contract. Subtract the Fwd FX if you are long and Add it if you are shot and then take the current FX rates (that lead to lowest spread) * basis points for growth then discount back

<p>You are always in a position to make the LEAST spread. Pay attention to whether you are long or short a contract. Subtract the Fwd FX if you are long and Add it if you are shot and then take the current FX rates (that lead to lowest spread) * basis points for growth then discount back</p>
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<p><span>mark-to-market value of the original forward contract</span></p>

mark-to-market value of the original forward contract

1. Identify the Original Forward Rate (F0F_0)

  • Original Forward Rate (F0F_0): 1.4301 EUR/CAD1.4301 \text{ EUR/CAD}

  • Notional Amount: 1,000,000 CAD1,000,000 \text{ CAD} (Base currency)

2. Calculate the New Forward Rate (FtF_t)

Since the investor originally bought CAD (long CAD), closing out the position requires selling CAD (short CAD). You must take the bid side of the market for both the spot rate and the forward points:

  • Current Spot Bid: 1.40111.4011

  • 6-Month Forward Points (Bid): 46 points=4610,000=0.004646 \text{ points} = \frac{46}{10,000} = 0.0046

Ft=Spot Bid+Forward Points=1.4011+0.0046=1.4057 EUR/CADF_t = \text{Spot Bid} + \text{Forward Points} = 1.4011 + 0.0046 = 1.4057 \text{ EUR/CAD}

3. Calculate the Future Cash Flow at Settlement

Subtract the original buy rate from the new sell rate, then multiply by the contract size:

Cash Flow at Settlement=(1.4057−1.4301)×1,000,000=−0.0244×1,000,000=−€24,400\text{Cash Flow at Settlement} = (1.4057 - 1.4301) \times 1,000,000 = -0.0244 \times 1,000,000 = -\text{€}24,400

4. Discount the Future Cash Flow to Present Value

Discount the settlement cash flow back 180 days180 \text{ days} (6 months) using the 180-day MRR for the price currency (EUR) at 2.5% annualized2.5\% \text{ annualized}:

Present Value=−€24,4001+(0.025×180360)=−€24,4001+0.0125=−€24,4001.0125≈−€24,098.76\text{Present Value} = \frac{-\text{€}24,400}{1 + \left(0.025 \times \frac{180}{360}\right)} = \frac{-\text{€}24,400}{1 + 0.0125} = \frac{-\text{€}24,400}{1.0125} \approx -\text{€}24,098.76

Rounded to the nearest euro, the mark-to-market value is EUR –24,099

<p>1. Identify the Original Forward Rate (<span>$F_0$</span>)</p><ul><li><p><strong>Original Forward Rate (</strong><span><strong>$F_0$</strong></span><strong>):</strong> <span>$1.4301 \text{ EUR/CAD}$</span></p></li><li><p><strong>Notional Amount:</strong> <span>$1,000,000 \text{ CAD}$</span> (Base currency)</p></li></ul><p>2. Calculate the New Forward Rate (<span>$F_t$</span>)</p><p>Since the investor originally bought CAD (long CAD), closing out the position requires <strong>selling CAD</strong> (short CAD). You must take the <strong>bid</strong> side of the market for both the spot rate and the forward points:</p><ul><li><p><strong>Current Spot Bid:</strong> <span>$1.4011$</span></p></li><li><p><strong>6-Month Forward Points (Bid):</strong> <span>$46 \text{ points} = \frac{46}{10,000} = 0.0046$</span></p></li></ul><p>$$F_t = \text{Spot Bid} + \text{Forward Points} = 1.4011 + 0.0046 = 1.4057 \text{ EUR/CAD}$$</p><p>3. Calculate the Future Cash Flow at Settlement</p><p>Subtract the original buy rate from the new sell rate, then multiply by the contract size:</p><p>$$\text{Cash Flow at Settlement} = (1.4057 - 1.4301) \times 1,000,000 = -0.0244 \times 1,000,000 = -\text{€}24,400$$</p><p>4. Discount the Future Cash Flow to Present Value</p><p>Discount the settlement cash flow back <span>$180 \text{ days}$</span> (6 months) using the 180-day MRR for the price currency (EUR) at <span>$2.5\% \text{ annualized}$</span>:</p><p>$$\text{Present Value} = \frac{-\text{€}24,400}{1 + \left(0.025 \times \frac{180}{360}\right)} = \frac{-\text{€}24,400}{1 + 0.0125} = \frac{-\text{€}24,400}{1.0125} \approx -\text{€}24,098.76$$</p><p>Rounded to the nearest euro, the mark-to-market value is <strong>EUR –24,099</strong></p>
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aggregate value of the stocks

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Growth rate in potential GDP

Long-term growth rate of labor force + Long-term growth

rate in labor productivity.

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Capital deepening given Labour productivity growth and TFP growth

Country A’s labor productivity grew by 2.4% per year, of which 0.6% came from TFP growth and 1.8% from capital deepening (2.4% − 0.6% = 1.8%).