Suppose You Are Asked To Advise A Risk-Averse Individual

Suppose You Are Asked To Advise A Risk Avert Individual Who Is To

Suppose you are asked to advise a risk-averse individual who is to invest $50 million for one year either in the U.S. or in the U.K., given the following information: iu.s. = 5%; iu.k. = 4%; Spot exchange rate = 1.5 dollars per pound; and the one-year forward exchange rate = 1.3 dollars per pound. Additionally, the model of the economy is represented by the equations: 1. Y = C + I + G + X - M; 2. C = 200 + 0.8Y; 3. I, G, X, M are not specified but are part of the model. The questions include calculating equilibrium income, open economy multiplier, consumption, saving, imports at equilibrium, and analyzing the balance of payments, fiscal policy effects, and trade impacts based on changes in government spending, exports, and interest rates.

Paper For Above instruction

Advising a risk-averse individual on international investment opportunities requires careful consideration of both macroeconomic factors and currency risks. When contemplating investing $50 million for one year in either the United States or the United Kingdom, the decision hinges on interest rates, exchange rates, and expectations about future currency movements. This analysis leverages the given data and economic models to provide a comprehensive recommendation.

Economic Context and Key Variables

The interest rates in the U.S. and U.K. are 5% and 4%, respectively, indicating slightly lower borrowing costs in the U.K. The current spot exchange rate is 1.5 dollars per pound, and the one-year forward rate is 1.3 dollars per pound. The forward rate’s deviation from the spot rate signals expected currency appreciation of the pound against the dollar. For a risk-averse investor, this expectation of currency movement influences the decision, as currency fluctuations can significantly affect returns.

Investment Analysis Based on Interest Rates and Forward Exchange Rate

The initial consideration is the forward exchange rate relative to the spot rate. Since the forward rate (1.3) is lower than the spot rate (1.5), it suggests that the pound is expected to appreciate relative to the dollar over the next year. From an interest rate parity (IRP) standpoint, the implied expected appreciation should be close to the difference in interest rates, but actual currency markets may reflect additional risk premiums or market expectations.

Using the interest rate parity condition, the expected future exchange rate (E[S]) can be approximated by:

E[S] = S × (1 + iu.u.s.) / (1 + iu.u.k.) = 1.5 × (1 + 0.05) / (1 + 0.04) ≈ 1.5 × 1.05 / 1.04 ≈ 1.51

This expectation suggests the dollar may weaken slightly relative to the pound, or equivalently, the pound appreciates. Since the forward rate (1.3) indicates a higher expected pound value, the market might be pricing in additional premium for currency stability or other factors.

Currency Risk and Return Calculation

For a risk-averse investor, the decision depends on the net return after adjusting for exchange rate movements. The basic return in the U.S. is:

Return in U.S. = interest rate = 5%. If the dollar depreciates less than anticipated or remains stable, the net gain is primarily from the interest.

For the U.K., the nominal interest rate is 4%, but the expected appreciation of the pound (based on forward rate and IRP) could mean the investor gains from currency movements. The effective return in GBP considering currency appreciation is:

Effective return in GBP = 4% + (Expected appreciation of GBP). Since the expected appreciation is roughly 1% (from 1.5 to 1.51), the approximate total return in GBP is 5%.

Optimal Investment Choice

Given the risk-averse nature, the individual should prefer the investment with the lower currency and market risk. The U.S. investment offers a slightly higher interest rate (5% vs. 4%) but exposes the investor to dollar depreciation risk if the dollar weakens unexpectedly. Conversely, investing in the U.K. offers a lower nominal interest rate but a higher expected currency appreciation, which can offset the lower interest rate gains.

Considering all factors, the optimal advice depends on the investor's risk tolerance and view on currency stability. If the investor prioritizes stability and minimal currency risk, investing in the U.S. might be preferred despite the slightly higher interest rate. However, if the investor expects the pound to appreciate as indicated, investing in the U.K. offers a better risk-adjusted return, especially given the forward rate signals markets' expectations of currency movements.

Implications for the Macroeconomic Model and Policy

The second part of the analysis involves the macroeconomic equations and their implications. The model Y = C + I + G + X - M, with consumption C = 200 + 0.8Y, and other components, highlights the equilibrium income level, the open economy multiplier, and the effects of fiscal and monetary policies.

Calculating equilibrium income involves setting the planned expenditure equal to output. Without explicit values for I, G, X, and M, qualitative assessments suggest that an increase in autonomous spending (consumption, investment, or exports) raises equilibrium income. The multiplier effect indicates how changes in autonomous expenditure influence total income; a higher marginal propensity to consume (0.8) amplifies this effect.

Fiscal policy adjustments, like changing government spending G, directly impact income and trade balance. An increase in G stimulates aggregate demand, raising income but potentially worsening the trade balance if imports also increase. Conversely, reducing G narrows the trade deficit or improves the surplus. The balance of payments depends on the difference between exports and imports; an excess of imports over exports results in a deficit.

Impact of Policy Changes and External Shocks

In the macroeconomic framework, an increase in exports by 10 units due to foreign demand enhances income and reduces trade imbalance. Conversely, if the Fed cuts interest rates, it lowers the cost of borrowing, encouraging investment but potentially weakening the currency. When interest rates fall from 0.10 to 0.15, the cost of funds decreases, leading to higher investment, which increases aggregate demand and income. However, a lower interest rate can also lead to currency depreciation, making exports more competitive, further boosting the trade balance.

If the government simultaneously cuts spending by 100 units and the Fed lowers interest rates to 0.05, the net effect on income depends on the magnitude of fiscal contraction offset by monetary expansion. Generally, the fiscal contraction reduces aggregate demand, but the monetary policy easing aims to offset this, leading to a potentially neutral or slightly expansionary outcome depending on the sensitive multipliers involved. Precise calculations would require explicit values for the marginal propensity to consume and the marginal efficiency of investment.

Conclusion

In advising the risk-averse investor, a careful analysis of interest rates, exchange rates, and currency expectations guides the optimal decision. Fundamental macroeconomic models support the idea that policy measures influence income, trade balance, and overall economic stability. Understanding these dynamics enables policymakers and investors to make informed decisions that balance risk, return, and macroeconomic stability.

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