Suppose You Invested 1,000,000 In England Last Year

Suppose That You Invested 1000000 In England Last Year And The Val

Suppose that you invested £1,000,000 in England last year, and the value of your investment increased to £1,100,000 this year. At the same time, BP has depreciated from $1.75/£ to $1.55/£. Calculate the pound return (percent) and the dollar return (percent) on this investment from last year to this year. Explain the concepts of a factor model presented in the equation: r_j = m_j + b_1jF₁ + b_2jF₂ + b_3jF₃ + b_4jF₄ + e_j. Explain why this model has advantages over a market model: r_j = a_j + b_jr_M + e_j. If you add one more factor to estimate the return of a foreign asset, which variable should you add to the equation: r_j = m_j + b_1jF₁ + b_2jF₂ + b_3jF₃ + b_4jF₄ + e_j? Explain why.

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The investment of £1,000,000 in England last year, which appreciated to £1,100,000 this year, represents a 10% increase in the value of the investment. To quantify the returns, we first analyze the pound return, which measures the percentage change in investment value in the local currency. The pound return is calculated as [(final value - initial value) / initial value] × 100, which results in [(£1,100,000 - £1,000,000) / £1,000,000] × 100 = 10%. This indicates that the investment in pounds appreciated by 10% over the year.

Next, to determine the dollar return, it is essential to consider the change in the exchange rate because the value of the investment in dollars depends on both the investment’s value in pounds and the exchange rate. Initially, the exchange rate was $1.75/£, so the initial investment in dollars was £1,000,000 × $1.75/£ = $1,750,000. At the end of the year, when the investment increased in pounds to £1,100,000 and the exchange rate moved to $1.55/£, the value in dollars is £1,100,000 × $1.55/£ = $1,705,000.

The dollar return is thus calculated as [(final dollar value - initial dollar value) / initial dollar value] × 100, which equates to [( $1,705,000 - $1,750,000) / $1,750,000] × 100 ≈ -2.57%. Despite the investment appreciating in pounds, the depreciation of the dollar against the pound resulted in a negative dollar return.

The concepts of factor models are fundamental in asset return analysis, providing a way to decompose asset returns into components driven by observable factors. The model presented (r_j = m_j + b_1jF₁ + b_2jF₂ + b_3jF₃ + b_4jF₄ + e_j) attributes an asset’s return to sensitivities (b coefficients) to various factors (F₁ to F₄) and an intercept term (m_j). This multi-factor approach improves over single-factor models by capturing multiple sources of return variation, like inflation, interest rates, and foreign exchange rates, that influence an asset’s performance indirectly or directly.

The advantage of the multi-factor model over a simple market model (r_j = a_j + b_jr_M + e_j) lies in its ability to incorporate several systematic risk factors beyond just market risk. While the market model attributes return variations solely to overall market movements, the multi-factor model can include various macroeconomic and financial variables, allowing for a more nuanced understanding of what drives asset returns and improving prediction accuracy (Fama & French, 1993).

When including an additional factor to estimate the return of a foreign asset, the variable most logical to add is a currency risk factor or exchange rate risk variable, such as the change in the foreign currency’s spot rate or an exchange rate index. This is because fluctuations in foreign exchange rates significantly impact the returns of foreign assets, especially when they are not perfectly hedged. Incorporating exchange rate risk helps in capturing the contribution of currency movements to the total return, enabling more accurate asset valuation, risk assessment, and portfolio optimization (Engel, 2014).

In conclusion, understanding the translation of returns in different currencies, the comparative advantages of multi-factor models, and the importance of including relevant risk factors such as exchange rates are vital aspects of international asset management and risk assessment. These insights help investors better comprehend the complex dynamics affecting their investments across geopolitical and economic boundaries, leading to more informed decision-making and optimized portfolio strategies (Chen & Zhao, 2020).

References

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