Lecture 6 Notes on International Finance

Uncovered Interest Parity (UIP)

• UIP is a financial market theory focused on arbitrage in bond markets, distinct from LOOP and PPP which focus on goods markets.
• Formula for UIP:
  • $i<em>t = i^*</em>{t} + \frac{S<em>{e</em>{t+1}} - S<em>t}{S</em>t}$
  • Where:
    • $i_t$ = nominal interest rate on domestic bonds at time $t$
    • $i^*_{t}$ = nominal interest rate on foreign bonds at time $t$
    • $\frac{S<em>{e</em>{t+1}} - S<em>t}{S</em>t}$ = expected exchange rate depreciation/appreciation of domestic currency.
• At investment time, investors should feel indifferent between domestic and foreign bonds, hence:
  • $1 + i<em>t = (1 + i^*</em>{t}) \frac{S<em>{e</em>{t+1}}}{S_t}$
• A property of the natural logarithm allows for simplification under conditions where $x \leq 20\%$, leading to:
  • $\ln(1 + i<em>t) \approx i</em>t$
  • This implies:
  • $i<em>t = i^*</em>{t} + \text{Expected capital gain/loss on } S$

Key Concepts Surrounding UIP

• Return Equivalence: Certain return on home bonds equals expected return on foreign bonds (includes expected capital gain/loss on exchange rate).
• Expected depreciation of the domestic exchange rate indicates expected capital gain from foreign bonds; appreciation denotes loss.
• Expectations Impact:
  • Future expectations about exchange rates significantly influence current spot rates ($S_t$):
  • $S<em>t = \frac{S</em>{e<em>{t+1}}}{1 + i</em>t - i^*_t}$
• UIP Assumptions:
  1. Perfect capital mobility guarantees unrestricted arbitrage.
  2. Non-risky bonds with known interest rates ensure fair comparison.
  3. Home and foreign bonds treated as perfect substitutes ensures investor rationality.

Introduction to Monetary Models of Exchange Rates

• Monetary models treat money supply and demand as determining factors for exchange rates. UIP is assumed to hold.
• Models vary on price flexibility:
  • Flexible Prices: Purchasing Power Parity (PPP) holds in short and long term.
  • Sticky Prices: PPP holds only in the long run.

Money Demand and Supply

• Money Demand: Negatively related to interest rates (opportunity cost of holding money).
• Money Supply: Controlled by central banks; equilibrium is achieved when money supply equals money demand.
• Monetary Policy: Central banks manipulate money supply to influence equilibrium interest rates, which ultimately affects exchange rates.

Flex-Price Monetary Model of the Exchange Rate

• Assumes perfectly flexible prices, relevant during times of high inflation or in the long run.
• The model connects exchange rate movements with money supply indicating countries with high money supply growth typically see currency depreciation.
• Key Equations:
  • Domestic demand for real money balances:
  • $m<em>{d</em>t} - p<em>t = \eta y</em>t - \sigma i_t$
  • Equilibrium in money market:
  • $m<em>d = m</em>t$
  • Purchasing Power Parity:
  • $s<em>t = p</em>t - p^*_t$
  • Final equation predicting the nominal exchange rate:
  • $s<em>t = m</em>t - m^<em><em>t - \eta(y</em>t - y^</em><em>t) + \sigma(i</em>t - i^*_t)$

Implications of the Flex-Price Model

1. Rate of Depreciation:
   • $s<em>t - s</em>{t-1} = m<em>t - m</em>{t-1} - (m^<em><em>t - m^</em></em>{t-1})$
2. GDP Growth Impact:
   • Holds that equilibrium outcomes differ when interest rates and money supplies remain static versus under growth.
3. Expectations:
   • Expected future depreciation potentially alters current valuations, showing dynamic effects of market sentiments on exchange rates.

Dornbusch Model

Motivation

• The model distinguishes between flexible and sticky prices, addressing the significant volatility of exchange rates due to temporary rigidities in goods prices.
• Overshooting: Indicates that due to initial rigidities in prices, exchange rates can overshoot long-term equilibrium, reflecting rapid adjustments in financial markets versus slower adjustments in goods markets.

Conclusions

• The Dornbusch model enhances the understanding of short-run deviations from PPP and highlights the role of arbitrage in financial markets influencing exchange rates.
• Empirical evidence supports the notions that exchange rates behave differently than goods prices due to the timing and nature of market responses.