The price of the base currency expressed in terms of the price currency.
Spot exchange rate: currency exchange rates for immediate delivery.
Forward exchange rate: currency exchange rates for an exchange to be done in the future.
Bid price and offer price
Bid price买入价: the price that a dealer做市商愿意买入右币的价格 will pay per base currency unit.
Offer price卖出价: the price that a dealer做市商愿意卖出右币的价格 will sell a unit of base
currency.
The offer price is always higher than the bid price.
The counterparty of a dealer is to have either hit the bid(sell the base currency 毕业生美元换人民币) or paid the offer (buy the base currency 留学生人民币换美元).
The bid-offer spread: The difference between the offer and bid price.
Spreads are often stated as 'pips', except yen.
Example: the USD/EUR could be quoted as $1.4124~1.4128.The spread is $0.0004(4 pips).
The bid-offer spread a dealer provides to its clients is typically wider than the bid-offer spread in the interbank market.
The spread quoted by a dealer to its clients depends on:
bid-ask spread quoted in the interbank market. 与interbank的spread联动
size of the transaction. 单笔交易量越大，风险越高，spread越大
relationship between the dealer and client.
Interbank spreads depend on:
currency pair involved.
time of day.
market volatility.
FX Caculation
Cross rate calculation
\begin{aligned} & \left(\frac{\mathrm{A}}{\mathrm{B}}\right)_{b i d}=\left(\frac{\mathrm{A}}{\mathrm{C}}\right)_{b i d}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)_{b i d} \\ & \left(\frac{\mathrm{~A}}{\mathrm{~B}}\right)_{a s k}=\left(\frac{\mathrm{A}}{\mathrm{C}}\right)_{a s k}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)_{a s k} \\ & \left(\frac{\mathrm{~A}}{\mathrm{~B}}\right)_{b i d}=1/\left(\frac{\mathrm{B}}{\mathrm{A}}\right)_{a s k} \\ & \left(\frac{\mathrm{~A}}{\mathrm{~B}}\right)_{a s k}=1/\left(\frac{\mathrm{B}}{\mathrm{A}}\right)_{b i d}\end{aligned}
计算原则为使结果的左右差值最大化，即左为小除以大或小乘以小，右为大除以小或大乘以大
Triangular arbitrage
Triangular arbitrage: If identical financial products are priced differently, then market participants will buy the cheaper one and sell the more expensive one until the price difference is eliminated.
The bid quoted by a dealer in the interbank market cannot be higher than the current interbank offer. The offer quoted by a dealer in the interbank market cannot be lower than the current interbank bid. Interbank和Dealer的报价区间不重合就能套利, 间隔就是单位套利值
The cross-rate bids (offers) posted by a dealer must be lower(higher) than the implied cross-rate offers (bids) available in the interbank market. 根据Interbank市场计算交叉汇率，与Dealer报价比较
At a forward premium: 远期升水更升值; a forward discount: 远期贴水更贬值
升贴水形式：左高右低贴水（如30/20），左低右高升水（如20/50）
计算方式：使得结果的左右差值最大化，即贴水时小减大，升水时大加大
Mark-to-market value盯市价值: the profit (or loss) that would be realized from closing out the position at current market prices.
To close out a forward position, we must offset it with an equal and opposite forward position using the spot exchange rate and forward points available in the market when the offsetting position is created.
The process for marking to market a forward position: Step1: Create an offsetting forward position that is equal to the original forward position. Step2: Determine the appropriate all-in forward rate for this new, offsetting forward position. Step3: Calculate the cash flow at the settlement day. Step4: Calculate the present value of this cash flow at the future settlement date.The currency of the cash flow and the discount rate must match.
International parity
Overview of key international parity conditions
Interest rate parity
Covered interest rate parity(CIRP): an investment in a foreign money market instrument that is completely hedged against exchange rate risk should yield exactly the same return as an otherwise identical domestic money market investment.
F_{f/d}=S_{f/d}\times\frac{1+i_{f}\times\frac{\text{days}}{360}}{1+i_{d}\times\frac{\text{days}}{360}}
The domestic currency will trade at a forward premium if the foreign risk-free interest rate exceeds the domestic risk-free interest rate
Uncovered interest rate parity(UIRP): the change in spot rate over the investment horizon should, on average, equal the differential in interest rates between the two countries.
\begin{align}
&S^e_{f/d}=S_{f/d}\times\frac{1+i_{f}\times\frac{\text{days}}{360}}{1+i_{d}\times\frac{\text{days}}{360}}
\\
&\%\Delta S^e_{f/d}\approx (i_{f}-i_{d})\times\frac{\text{days}}{360}
\end{align}
The investor is assumed to be risk-neutral
The expected appreciation/depreciation of the exchange rate just offsets the yield differential.
FX carry trade
When UIRP does not hold, in a FX carry trade, an investor invests in a higher yielding currency using funds borrowed in a lower yielding currency(funding currency, d).
During periods of low volatility, carry trades tend to generate positive returns, but they are prone to significant crash risk in turbulent times.
Forward rate parity
Forward rate parity (FRP): the forward exchange rate will be an unbiased predictor of the future spot exchange rate if both covered and uncovered interest rate parity hold. 预期汇率是远期汇率的无偏估计
CIRP must hold because it is enforced by arbitrage.The question of whether FRP holds is thus dependent upon whether UIRP holds.
Purchasing power parity
Absolute PPP: the equilibrium exchange rate between two countries is determined entirely by the ratio of their national price levels.
S_{f/d}=\frac{P_f}{P_d}
In practice, absolute PPP might not hold because the weights of the various goods in the two economies may not be the same(e.g., people eat more potatoes in Russia and more rice in Japan)
Relative PPP: the percentage change in the spot exchange rate will be completely determined by the difference between the foreign and domestic inflation rate.
\%\Delta S_{f/d}=\frac{\pi_f-\pi_d}{\pi_d+1}\approx \pi_f-\pi_d
Ex-ante version of PPP asserts that the expected changes in the spot exchange rate are entirely driven by expected differences in national inflation rates.
\%\Delta S^e_{f/d}\approx \pi^e_f-\pi^e_d
Countries that are expected to run persistently high inflation rates should expect to see their currencies depreciate over time.
International Fisher effect
Fisher effect
i={r}+\pi^{{e}}
International Fisher effect(If UIRP and ex-ante PPP both hold)
i_f-i_d=\pi_f^e-\pi_d^e
r_f=r_d is called real interest rate parity(RIRP).
Summary
According to CIRP, arbitrage ensures that nominal interest rate spreads equal the percentage forward premium (or discount).
According to UIRP, the expected percentage change of the spot exchange rate should, on average, be reflected in the nominal interest rate spread.
If both CIRP and UIRP hold, then the forward exchange rate will be an unbiased predictor of the future spot exchange rate.
According to the ex ante PPP, the expected change in the spot exchange rate should equal the expected difference between domestic and foreign inflation rates.
Assuming the Fisher effect and RIRP hold in all markets, then the international Fisher effect holds.
If ex ante PPP and the international Fisher effect hold, then UIRP holds
FX and BOP
Overview of BOP flows
Over the long term, countries that run persistent current account deficits (net borrowers) often see their currencies depreciate because they finance their acquisition of imports through the continued use of debt. 经常账户影响长期
However, investment/financing decisions are usually the ominant factor in determining exchange rate movements, at east in the short to intermediate term. 资本账户影响短期
Influence of current account on exchange rates
Current account influences the path of exchange rates through the following mechanisms:
Country with persistent current account surpluses (deficits) would see their currencies appreciate (depreciate) over time.
The amount by which exchange rates must adjust to restore current accounts to balanced positions depends on:
The initial gap between imports and exports.
The response of import and export prices to changes in the exchange rate.
The response of import and export demand to the change in import and export prices.
Current account imbalances shift financial wealth from deficit nations to surplus nations.
Nations running large current account surpluses versus the United States might find that their holdings of US dollar-denominated assets exceed the amount they desire to hold in a portfolio context. Actions they might take to reduce their dollar holdings to desired levels could then have a profound, negative impact on the dollar's value.
Debt sustainability channel 逆差 -> 借债 -> 本币贬值
If a country runs a large and persistent current account deficit over time, eventually it will experience an untenable rise in debt owed to foreign investors.
If such investors believe that the deficit country's external debt is rising to unsustainable levels, they are likely to reason that a major depreciation of the deficit country's currency will be required at some point.
Influence of capital account on exchange rates
As capital flows into (out) a country, demand for that country's currency increases (decreases), resulting in appreciation (depreciation).
Global capital flows have helped fuel boom-like conditions in emerging market economies for a while before, suddenly and often without adequate warning, those flows reversed.
Excessive emerging market capital inflows often plant the seeds of a crisis by contributing to:
An unwarranted appreciation of the currency
A huge buildup in external indebtedness
An asset bubble
A consumption binge消费狂热 that contributes to explosive growth in domestic credit and/or the current account deficit
An overinvestment in risky projects and questionable activities
Equity market trends and exchange rates
Increasing equity prices can also attract foreign capital.
Instability in the correlation between exchange rates and equity markets makes it difficult to form judgments on possible future currency moves based solely on expected equity market performance.
FX and monetary/fiscal policy
Mundell-Fleming model
It describes how changes in monetary and fiscal policy within a country affect interest rates and economic activity, which in turn leads to changes in capital flows and trade and ultimately to changes in the exchange rate.
Assume inflation plays no role.
Mundell-Fleming approach focuses on the short-term implications of monetary and fiscal policy.
Monetary-fiscal policy mix with high capital mobility
Expansionary monetary policy → interest rate decrease → investments and spending increase → capital flows to high-yielding countries → depreciation pressure
Expansionary fiscal policy → spending increase or tax decrease → interest rate increase → capital flows being attracted from low-yielding countries → appreciation pressure
Monetary-fiscal policy mix with low capital mobility
Assume that output is fixed, so that monetary policy primarily through the price level and the rate of inflation.
Pure monetary model: assuming that purchasing power parity holds, a money supply-induced increase (decrease) in domestic prices relative to foreign prices should lead to a proportional decrease (increase) in the domestic currency's value. 宽松货币政策 -> 立刻通胀 -> 本币贬值(长期)
Dornbusch overshooting超调 model
Assumes prices have limited flexibility物价黏性 in the short run but are fully flexible in the long run.
Under an expansionary monetary policy, in the short term, exchange rates overshoot the long-run PPP implied values. The depreciation of currency is greater than the depreciation implied by PPP. In the long term, exchange rates gradually increase toward their PPP implied values. 宽松货币政策 -> 利率立刻下降并回升、通胀开始 -> 本币超额贬值(短期)再回升
Portfolio Balance Approach
Portfolio balance model focuses on the long-term implications of fiscal policy on currency values.
Continued increases in fiscal deficits are unsustainable and investors may refuse to fund the deficits. The government will have to monetize its debt (i.e., print money), leading to currency depreciation.
In the long term, the government has to reverse course (tighter budgetary policy) leading to depreciation of the domestic currency.
FX Management and Currency Crisis
Government intervention and capital controls
Capital flows can be both a blessing and a curse. Governments resist excessive inflows and currency bubbles by using capital controls and direct intervention (selling their currency) in the foreign exchange market.
Key issue for policymakers:
preventing currencies from appreciating too strongly
reducing the aggregate volume of capital inflows
enabling monetary authorities to pursue independent monetary policies
Effectiveness of direct government intervention
The effect of intervention in developed market economies is limited.
Emerging market central banks appear to be in a stronger position than their developed market counterparts to influence the level and path of their exchange rates.
Warning signs of a currency crisis
Prior to a currency crisis, the capital markets have been liberalized to allow the free flow of capital.
There are large inflows of foreign capital (relative to GDP) in the period leading up to a crisis, with short- term funding denominated in a foreign currency being particularly problematic.
Currency crises are often preceded by(and often coincide with) banking crises.
Countries with fixed or partially fixed exchange rates are more susceptible to currency crises than countries with floating exchange rates.
The ratio of exports to imports (known as "the terms of trade, ToT") often deteriorates before a crisis.
In the period leading up to a crisis, the currency has risen substantially relative to its historical mean.
Inflation tends to be significantly higher in pre-crisis periods compared with tranquil periods.
Foreign exchange reserves tend to decline precipitously as a crisis approaches.
Broad money growth and the ratio of M2(a measure of money supply) to bank reserves tend to rise prior to a crisis.
Economic Growth
Importance of economic growth
Some of the key institutions and requirements for growth
Savings and investment
Financial markets and intermediaries
Political stability, rule of law, and property rights
Education and health care systems
Tax and regulatory systems
Free trade and unrestricted capital flows
Why potential growth matters to equity investors
Relationship between economic growth and equity return: Grinold-Kroner(2002)
E(Re)
= dividend yield + expected capital gain
= dividend yield + expected repricing + earnings growth per share
= dividend yield + expected repricing + inflation rate + real economic growth + change in shares outstanding
= dy + ∆(P/E) + i + g + ∆S
E(Re) = dy + ∆(P/E) + i + g + ∆S, overtime:
dy: the dividend yield, fairly stable
∆(P/E): the expected repricing term, volatility in the market's P/E ratio over market cycles.
i+g+∆S: Earnings growth per share can be expressed as a function of inflation, real economic growth, and change in the number of shares traded in the market.
∆S: Net buybacks (nbb, 回购减增发，越大则E(Re)越大) + relative dynamism (rd, 中小型非上市公司数量，越小则E(Re)与g越相关)
Economic growth does not guarantee that existing equity investors capture the new wealth created.
Why potential growth matters to fixed income investors
Higher rates of potential GDP growth translate into higher real interest rates and higher expected real asset returns in general.
Potential GDP and its growth rate also affect:
general credit quality of fixed income securities.
the likelihood of a change in central bank policy.
credit risk of sovereign debt or government- issued debt.
the budgetary balance that would exist.
Production function
Cobb-Douglas production function
Production Function
Two-factor production function: Y = AF(K, L)
Cobb-Douglas production function: Y=AK^a L^{1-a}
A is total factor productivity, a is the share of GDP paid out to the suppliers of capital.
Two important properties:
Constant returns to scale规模报酬不变: increasing all inputs by a fixed percentage leads to the same percentage increase in output.
Diminishing marginal productivity边际报酬递减: at some point the extra output obtained from each additional unit of the input will decline, keeping the other inputs unchanged.
Output per worker or labor productivity:
Y / L=\left(A K^\alpha L^{1-\alpha}\right) / L=A(K / L)^\alpha\Rightarrow y=Ak^\alpha
A value of a close to zero means diminishing marginal returns to capital are very significant and the extra output made possible by additional capital declines quickly as capital increases. A越小，边际递减越明显
Capital deepening vs. technological progress
Capital deepening, an increase in the capital-to-labor ratio, is reflected in the exhibit by a move along the production function from point A to B.
From B to D, further additions to capital have relatively little impact on per capita output
Economy reaches steady state, where the marginal product of capital equals its marginal cost, capital deepening is useless.
From B to C, an improvement in TFP causes a proportional upward shift in the entire production function.
