4.3 Forward Points, the Carry Trade & Policy Effects on Exchange Rates

4.3 Forward Points, the Carry Trade & Policy Effects on Exchange Rates

How this fits: section 4.1 built the parity conditions and the long-run equilibrium models. This section covers the remaining learning outcomes of the Currency Exchange Rates module — forward premiums and discounts, marking a forward to market, carry trade profit, balance-of-payments flows, the monetary-fiscal policy mix, intervention, and capital controls. Level II tests these as calculation-plus-interpretation pairs inside a single FX vignette.

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1. Forward Premiums, Discounts, and Forward Points

Using the professional convention P/B (price currency per one unit of base currency), the forward premium or discount is:

$F_{P/B} - S_{P/B} = S_{P/B} \times \frac{(i_P - i_B) \times \frac{\text{Actual}}{360}}{1 + i_B \times \frac{\text{Actual}}{360}}$

Three consequences follow immediately, and each is a testable statement:

1. The sign is determined entirely by the interest rate differential $(i_P - i_B)$. If the price currency has the higher rate, the base currency trades at a forward premium.
2. Equivalently, the higher-yielding currency always trades at a forward discount against the lower-yielding one. This is a restatement of covered interest rate parity and is the reason a fully hedged foreign bond cannot out-earn a domestic bond of equal risk.
3. The differential is scaled by the actual day count over 360 for money-market currencies, so a 90-day and a 180-day forward on the same pair have different point values.

Forward points are the premium or discount expressed in pips. For a pair quoted to four decimal places the pip factor is 10,000; for JPY pairs quoted to two decimals it is 100.

Example. Spot USD/EUR = 1.0850. The 6-month (180-day) US rate is 4.20% and the euro rate is 2.60%.

• Differential term: $(0.0420 - 0.0260)(180/360) = 0.0080$
• Denominator: $1 + 0.0260(180/360) = 1.0130$
• Premium: $1.0850 \times (0.0080 / 1.0130) = 1.0850 \times 0.007897 = 0.008568$
• Forward rate: $1.0850 + 0.008568 = 1.09357$, quoted as +85.7 points

The euro is the base currency and the dollar carries the higher rate, so the euro trades at a forward premium. A dealer quotes this as "USD/EUR 1.0850, 6-month points +85.7".

Bid–offer on the forward is the sum of the spot bid–offer and the points bid–offer, and it widens with maturity, with the illiquidity of either currency, and in stressed markets. When calculating a client's all-in forward rate, take the bid points against the bid spot for a client selling the base currency and the offer points against the offer spot for a client buying it — always the side that is worse for the client.

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2. Marking a Currency Forward to Market

A forward has zero value at initiation and non-zero value thereafter. The mark-to-market value of a long base-currency forward position, expressed in the price currency, is:

$V_t = \frac{(F_{t} - F_{0}) \times \text{Contract size}}{1 + i_P \times \frac{\text{Days remaining}}{360}}$

where $F_0$ is the contracted forward rate and $F_t$ is the current forward rate to the original settlement date — not the current spot rate. The numerator is the gain in price-currency units at settlement; the denominator discounts it back at the price currency's interest rate over the days remaining.

Worked example. Three months ago a corporate treasurer bought EUR 5,000,000 forward against USD for settlement in 6 months at $F_0 = 1.0936$ (USD/EUR). Today, with 90 days remaining, the 90-day forward rate to that same settlement date is $F_t = 1.1080$ and the 90-day US rate is 4.10%.

• Gain at settlement: $(1.1080 - 1.0936) \times 5{,}000{,}000 = 0.0144 \times 5{,}000{,}000 = \text{USD } 72{,}000$
• Discount factor: $1 + 0.0410(90/360) = 1.01025$
• Mark-to-market value: $72{,}000 / 1.01025 = \textbf{USD } 71{,}269$

The two errors the exam sets up here are (a) comparing $F_0$ against today's spot instead of today's forward to the original maturity, and (b) discounting at the base-currency rate.

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3. The Carry Trade

The carry trade borrows in a low-yielding funding currency and invests in a high-yielding investment currency, keeping the position unhedged. Its logic is a direct bet against uncovered interest rate parity (UIP), which predicts that the high-yield currency will depreciate by exactly the interest differential, leaving no expected profit.

$\text{Carry return} \approx (i_{\text{invest}} - i_{\text{fund}}) + \%\Delta S_{\text{invest/fund}}$

Empirically UIP fails at short horizons — the forward rate bias — and high-yield currencies have historically appreciated or held steady more often than UIP implies, which is why the trade persists.

Example. A manager borrows JPY at 0.40% and invests in MXN at 9.80% for one year. The peso depreciates 3.1% against the yen over the year.

• Interest differential: $9.80% - 0.40% = 9.40%$
• Currency loss: $-3.10%$
• Net return: $\approx \textbf{6.30%}$

Had the peso instead fallen 11%, the trade would have lost about 1.6% — and losses of that kind arrive in clusters.

Risk characteristics worth memorising:

• Returns are negatively skewed with high kurtosis (fat tails): many small gains, occasional very large losses.
• The trade is short volatility in substance; it unwinds violently when risk appetite falls, because leveraged positions are closed simultaneously.
• This asymmetry is called crash risk, and it means a Sharpe ratio computed from carry returns overstates the risk-adjusted attractiveness of the strategy.

4. Balance of Payments Flows and the Exchange Rate

The current account and the financial account must offset each other. Their exchange-rate effects operate on different horizons.

Current account channels (slow, long-run):

1. Flow supply/demand mechanism. A country running a persistent current account deficit must sell its currency to buy imports, exerting downward pressure. The size of the required depreciation depends on the deficit relative to economic size, the openness of the economy, and the price elasticity of tradable goods — inelastic import demand means a larger depreciation is needed to close a given deficit.
2. Portfolio balance mechanism. Surplus countries accumulate claims on the deficit country. Eventually they rebalance away from that concentration, which weakens the deficit country's currency.
3. Debt sustainability mechanism. If a deficit is financed by borrowing, the external debt ratio rises until investors demand a risk premium and the currency must fall to a level consistent with a sustainable external position.

Financial account channels (fast, short-run): capital flows respond to interest differentials and expected returns within hours. This is why an unexpected policy rate change moves a currency instantly while a trade deficit moves it over years.

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5. The Monetary and Fiscal Policy Mix: Mundell–Fleming

Mundell–Fleming links policy to the exchange rate through capital flows and trade flows. The degree of capital mobility decides which effect dominates.

High capital mobility (developed markets)

The intuition: expansionary fiscal policy raises real interest rates by increasing borrowing, drawing capital in and strengthening the currency; expansionary monetary policy lowers rates, pushing capital out and weakening it. Where they conflict, the answer is genuinely indeterminate and any vignette answer choice claiming otherwise is wrong.

Low capital mobility

Trade flows dominate instead. Expansionary policy of either kind raises income and imports, worsens the trade balance, and depreciates the currency; restrictive policy of either kind appreciates it.

The monetary models

• Under the pure monetary approach with flexible prices, purchasing power parity holds continuously and money supply growth translates one-for-one into depreciation; output and rates play no role.
• Under the Dornbusch overshooting model, prices are sticky in the short run, so an unanticipated monetary expansion drives the currency below its long-run PPP level before it appreciates back — the currency overshoots. This is the reason a rate cut can produce an immediate depreciation larger than the eventual equilibrium move.
• Under the portfolio balance model, sustained fiscal deficits eventually reverse the initial appreciation, because investors will not hold an ever-growing stock of the country's debt without a currency risk premium.

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6. Intervention and Capital Controls

Objectives of official intervention are to lower exchange rate volatility, to lean against short-term deviations from an estimated fair value, and — in emerging markets — to slow currency appreciation that would damage export competitiveness or to prevent a disorderly depreciation.

Effectiveness depends on the size of the central bank's reserves relative to daily turnover in its currency:

• In developed markets, official reserves are trivially small next to global FX turnover, and the evidence is that intervention has little sustained effect on the level of the rate. It can still reduce short-term volatility.
• In emerging markets, reserves are frequently large relative to a thin domestic FX market, so intervention can move the rate measurably in the short run. Even there, intervention that fights fundamentals eventually fails, as repeated peg collapses demonstrate.

Capital controls — taxes on inflows, minimum holding periods, quantitative limits, or restrictions on convertibility — are used when a country wants to run an independent monetary policy while managing its exchange rate. They partially resolve the impossible trinity: a country cannot simultaneously have a fixed exchange rate, free capital movement, and an independent monetary policy. Controls buy time; the evidence on their long-run effectiveness is mixed, and they raise the cost of capital for domestic borrowers.

Warning signs to watch alongside these tools include a rapidly widening current account deficit, a deteriorating ratio of short-term external debt to reserves, an appreciating real exchange rate combined with a fixed nominal rate, rapid domestic credit growth, and a boom followed by a bust in equity or property prices. Section 4.1 develops the full crisis checklist; here the point is that intervention and controls are the two policy instruments a central bank reaches for once those signals appear.