CFA 2018 Level 2 Economics
3 months ago
2017CFA 二级培训项目 Economics 讲师：单晨玮Topic Weightings in CFA Level II Session NO. Content Weightings
Study Session 1-2 Ethics & Professional Standards 10-15
Study Session 3 Quantitative Methods 5-10
Study Session 4 Economic Analysis 5-10
Study Session 5-6 Financial Statement Analysis 15-20
Study Session 7-8 Corporate Finance
5-15 Study Session 9-11
Equity Analysis 15-25
Study Session 12-13 Fixed Income Analysis 10-20
Study Session 14 Derivative Investments 5-15
Study Session 15 Alternative Investments 5-10 Study Session 16-17 Portfolio Management 5-10SS4 Economics for Valuation Framework
1. R13 Currency exchange rate: determination and forecastingEconomic Analysis
2. R14 Economic Growth and investment decision
3. R15 Economics of Regulation
1. Currency Exchange Rates
2. Spot Rate And Forward RateFramework
3. Bid-Ask Spread
4. Cross Rate
5. Triangular Arbitrage
6. Forward Discount And Premium
7. Mark-to-market value
8. The International Parity Relationships
9. Balance-of-Payments Accounts
10. FX Carry Trade
11. Exchange Rate Determination Models
Exchange rate is simply the price or cost of units of one currency in terms of another. Nominal exchange rate: the price that we observe in the marketplace for foreign exchange. Real exchange rate: the focus shifts from the quotations in the foreign exchange market to what the currencies actually purchase in terms of real goods and services.
FX real(d/f) = FX nominal (d/f) *CPI
Changes in real exchange rates can be used when analyzing economic changes over time.
When the real exchange rate (d/f) increases, exports of goods and services have gotten relatively less expensive to foreigners, and imports of goods and services from the foreign country have gotten relatively more expensive over timeExample: At a base period, the CPIs of the U.S. and U.K. are both 100, and the exchange rate is $1.70 per euro. Three years later, the exchange rate is $1.60 per euro, and the CPI has risen to 110 in the U.S. and 112 in the U.K.. What is the real exchange rate? Solution: The real exchange rate is $1.60 per euro * 112/110 = $1.629 per euro.
Warm-up: FX Appreciation and Depreciation Example: the dollar-Swiss franc rate increase from USD: CHF = 1.7799 to 1.8100. The Swiss franc has depreciated relative to the dollar – it now takes more Swiss francs to buy a dollar. An increase in the numerical value of the exchange rate means that the base currency has appreciated and that the price currency depreciated. 1.7799CHF/USD to 1.8100CHF/USD USD appreciated therefore CHF depreciated
Spot rates are exchange rates for immediate delivery of the currency.
Spot markets refer to transactions that call for immediate delivery of the currency. In practice, the settlement period is two business days after the trade date.
Forward rates are exchange rates for currency transactions that will occur in the future.
Forward markets are for an exchange of currencies that will occur in the futures. Both parties to the transaction agree to exchange one currency for another at a specific future date.
The spread on a foreign currency quotation
The bid price is smaller and listed first. It is the price the bank/dealer will pay per FC unit.
The ask price is higher and always listed second. It is the price at which the bank will sell a unit of FC.
The difference between the offer and bid price is called the spread.
Spreads are often stated as ‘pips’.
Example: the euro could be quoted as $1.4124-1.4128. The spread is $0.0004 (4 pips).
The spread on a forward foreign currency quotation Consider a 6-month (180 days) forward exchange rate quote from a U.S. currency dealer of GBP:USD = 1.6384 / 1.6407. spread = (1.6407
– 1.6384) = 0.0023 (23 pips) The spread quoted by the dealer depends on
The spread in the interbank market for the same currency pair. Dealer spreads vary directly with spreads quoted in the interbank market.
The size of the transaction. Larger, liquidity-demanding transactions generally get quoted a larger spread.
The relationship between the dealer and client. Sometimes dealers will give favorable rates to preferred clients based on other ongoing business relationships.
The interbank spread on a currency pair depends on
Currencies involved. Similar to stocks, high-volume currency pairs (e.g., USD/EUR, USD/JPY, and USD/GBP) command lower spreads than do lower-volume currency pairs (e.g., AUD/CAD).
Time of day. The time overlap during the trading day when both the New York and London currency markets are open is considered the most liquid time window; spreads are narrower during this period than at other times of the day. Market volatility. Higher volatility leads to higher spreads to compensate market traders for the increased risk of holding those currencies.
Spreads in forward exchange rate quotes increase with maturity. Calculate cross rate 方法2 (USD:NZD)/(USD:IDR)=IDR:NZD
IDR:NZD=0.00067 求 IDR:NZD 方法1
方法3 则1USD=2400 IDR，1USD=1.6 NZD
2400IDR /USD ，1.6 NZD/USD
联立得 2400 IDR=1.6 NZD， 求NZD/IDR? 则1 IDR=1.6/2400 NZD
因此， 1.6/2400NZD/IDR即 因此，IDR:NZD=0.00067
Calculate cross rate with bid-ask spreads
Example1: AUD: USD = 0.6000 - 0.6015 USD: MXN =10.7000 - 10.7200 此时应当左右两边相乘，得 AUD: MXN = 6.4200 – 6.4481 Example2: USD: SFR =1.5960
– 70 USD: ASD =1.8225 – 35，求SFR:ASD 此时应当下式除以上式，交叉， 得：SFR: ASD=1.1412 – 1.1425 Triangular arbitrage means converting from currency A to currency B, then from currency B to currency C, then from currency C back to A. If we end up with more of currency A at the end than we started with, we've earned an arbitrage profit.
Example: AUD: USD=0.6000 - 0.6015 USD: MXN=10.7000 - 10.7200 AUD: MXN=6.3000 - 6.3025 How to arbitrage from these markets? 0.6000-0.6015USD/AUD (1) 10.700-10.720MXN/USD (2)
Step One: 1$(1) → 1/0.6015AUD(3) → (1/0.6015)*6.3000MXN(2) →
((1/0.6015)*6.3000)/10.720USD → 0.97704USD Step Two: 1$(2) → 1*10.700MXN(3) → (1*10.700)/6.3025AUD(1) →((1*10.700)/6.3025)*0.6000USD → 1.01864USD Mehmet is looking at two possible trades to deter mine their profit potential. The first trade involves a possible triangular arbitrage trade using the Swiss, U.S. and Brazilian currencies, to be executed based on a dealer’s bid/offer rate quote of 0.5161/0.5163 in CHF/BRL and the interbank spot rate quotes presented in the following Exhibit. Based on Exhibit, the most appropriate recommendation regarding the triangular arbitrage trade is to: A. decline the trade, no arbitrage profits are possible.
B. execute the trade, buy BRL in the interbank market and sell it to the dealer.
C. execute the trade, buy BRL from the dealer and sell it in the interbank.
Currency Pair Bid/Offer
CHF/USD 0.9099/0.9101 BRL/USD 1.7790/1.7792
Forward discount or premium
With the convention of giving the value of the quoted currency (the first currency) in terms of units of the second currency, there is a premium on the quoted currency when the forward exchange rate is higher than the spot rate and a discount otherwise. Example: One month forward rate is EUR: USD=1.2468, the spot rate is 1.2500, it is a discount for EUR When a trader announces that a currency quotes at a premium, the premium should be added to the spot exchange rate to obtain the value of the forward exchange rate. The forward premium or discount
forward prmium =F-S or discount for Y
Given the following quotes for AUD/CAD, compute the bid and offer rates for a 30- day forward contract. Correct Answer:
Since the forward quotes presented are all positive, the CAD (i.e., the base currency) is trading at a forward premium.
30-day bid = 1.0511 + 3.9/10,000 = 1.05149 30-day offer = 1.0519 + 4.1/ 10,000 = 1.05231 The 30-day forward quote for AUD/CAD is 1.05149/1.05231.
Spot 1.0511/1.0519 30-day +3.9/+4.1 90-day +15.6/+16.8 180-day +46.9/+52.3
Mark-to-market value of a forward contract
The value of the forward contract will changes as forward quotes for the currency pair change in the market.
The value of a forward contract (to the party buying the base currency) at maturity (time T) is ： The value of a forward currency contract prior to expiration is also known as the mark-to-market value.
V FP FP contract size
360 T t FP FP contract size
Yew Mun Yip has entered into a 90-day forward contract long CAD 1 million against AUD at a forward rate of 1.05358 AUD/CAD. Thirty days after initiation, the following AUD/CAD quotes are available
The following information is available (at t=30) for AUD interest rates：
30-day rate： 1.12% 60-day rate： 1.16% 90-day rate： 1.20%
Spot 1.0612/1.0614 30-day +4.9/+5.2 60-day +8.6/+9.0 90-day +14.6/+16.8 180-day +42.3/+48.3
What is the mark-to-market value in AUD of Yip's forward contract? Correct Answer:
The forward bid price for a new contract expiring in T - t = 60 days is 1.0612 + 8.6/10,000 = 1.06206.
The interest rate to use for discounting the value is also the 60-day AUD interest rate of l.16%
1.06206 1.05358 1, 000, 000 8, 463.64
1 1 0.0116 360
T 360 T FP FP contract size
V days R
Interest Rate Parity Covered Interest Rate Parity Uncovered Interest Rate Parity International Fisher Relation PPP
Absolute PPP Relative PPP Ex-Ante Version of PPP
Covered Interest rate parity (IRP)
The word 'covered’ in the context of covered interest parity means bound by arbitrage.
Covered interest rate parity holds when any forward premium or discount exactly offsets differences in interest rates, so that an investor would earn the same return investing in either currency.
Interest rate parity relationship: Interest differential ≈forward differential
F (forward), S (spot) X/Y, r and r is the nominal risk-free rate in X and Y
1 X S r
F S 1 r r r X X Y 1 r r X Y S
1 r 1 r Y Y
Covered interest arbitrage is a trading strategy that exploits currency position when the interest rate parity equation is not satisfied.
When currencies are freely traded and forward contracts are available in the marketplace, interest rate parity must hold.
If it does not hold, arbitrage trading will take place until interest rate parity holds with respect to the forward exchange rate.
You can check for an arbitrage opportunity by using the covered interest differential, which says that the domestic interest rate should be the same as the hedged foreign interest rate.
1 r F
Y 1 r cov ered int erest differential
The difference between the domestic interest rate and the hedged foreign interest rate (covered interest differential) should be zero.
Assume a one year horizon. The risk-free assets are typically bank deposits
/ / / ( ) 360
骣 轾 琪 - 犏
F S Actual S r
X Y Y Actual r r
quoted using LIBOR for the currency involved. The day count convention is Actual/360.
犏 臌 = 琪
琪+ 犏 琪
F S Actual
X Y Y Actual
X X Y
1 360 1 360
犏 琪 犏 臌 桫
琪 犏 臌 = 琪 轾犏 琪 犏 臌 桫
Example: Calculating the forward premium (discount)
The following table shows the mid-market (average of the bid and offer) for the current CAD/AUD spot exchange rate as well as for AUD and CAD 270-day LIBOR (annualized):
Spot (CAD/AUD) 1.0145 270-day LIBOR (AUD) 4.87% 270-day LIBOR (CAD) 1.41%
The forward premium (discount) for a 270-day forward contract for CAD/AUD would be closest to:
A. - 0.0346
B. - 0.0254
Correct Answer: B The equation to calculate the forward premium (discount) is:
犏 琪 犏 臌 = 琪 轾 琪
/ / / ( ) 360
1 360 270 (0.0141 0.0487) 360 1.0145
CAD AUD CAD AUD CAD AUD CAD AUD AUD Actual r r
F S S Actual r
骣 轾 琪
犏 琪 犏 臌 桫
骣 轾 琪
犏 琪 犏 臌 =
0.0254 370 1 0.0487 360
= - 琪 轾 琪
犏 琪 犏 臌 桫If
If r r S then r r S r r S
X r r F then r r F r r S
X Y Y
X X Y
) ) 1 ( 1 ( S
Y be l profit wil the currency, borrow 1 ) 1 ( S
1 F Y
, 1 ) 1 ( F
1 ( F X borrow be l profit wil the currency,
1 F ) ) 1 (
The U.S. dollar interest rate is 8%, and the euro interest rate is 6%. The spot exchange rate is $ 1.30 per euro, and the forward rate is $ 1.35 per euro. Determine whether a profitable arbitrage exists, and illustrate such an arbitrage if it does. First we note that the forward value of the euro is " too high―. Interest rate>parity would require a forward rate of : $ 1.30 ( 1.08 / 1.06 ) = $ 1.3245 . The forward rate of $ 1.35 is higher than that implied by interest rate parity, and we should hold euros rather than hold dollars for a profitable arbitrage. The dollar is depreciating more than would be implied by interest rate parity. The steps in the covered interest arbitrage are:
Step1 : Borrow $ l,000 at 8% and purchased 1,000 / 1.30 = 769 . 23 euros.
Step2 : Invest the euros at 6% Step3
：Sell the expected proceeds at the end of one year, 769.23 ( 1.06 ) = 815.38 euros, forward 1 year at $ 1.35 each.
After one year :
Step1 : Sell the 815.38 euros under the terms of the forward contract at $1.35 to get $1,100.76.
Step2 : Repay the $ 1,000 8 % loan, which is $ 1,080. Step 3: Keep the difference of $ 20.76 as an arbitrage profit. Uncovered interest rate parity
If forward currency contracts are not available, or if capital flows are restricted so as to prevent arbitrage, the relationship need not hold. Uncovered interest rate parity refers to such a situation; uncovered in this context means not bound by arbitrage. Uncovered interest rate parity suggests that nominal interest rates reflect expected changes in exchange rates. The base currency is expected to appreciate (depreciate) by approximately
when the difference is positive (negative). Uncovered interest rate parity assumes that investors are risk-neutral.
X t Y r S E S r
Comparing covered and uncovered interest parity
Covered interest rate parity derives the no-arbitrage forward rate, while uncovered interest rate parity derives the expected future spot rate.
Covered interest parity is assumed by arbitrage. F = E(S
) If uncovered interest rate parity holds, the forward rate is an unbiased predictor of expected future spot rates.
Uncovered interest parity dose not hold in the short run, and it dose hold in the long run. So longer-term expected future spot rates based on uncovered interest rate parity are often used as forecasts of future exchange rates.
International Fisher relation The international Fisher relation specifies that the interest rate differential between two countries should be equal to the expected inflation differential. The condition assumes that real interest rates are stable over time and equal across international boundaries. The international Fisher relation is correct because differences in real interest rates between countries would encourage capital flows to take advantage of the differentials, ultimately equalizing real rates across countries.
International Fisher relation
e 1 r + 1 p +
1 r 1 p
r r p p
The relation between nominal interest rate and real interest rate:
Nom e Real
1 r (1 r )(1 )Law of one price : identical goods should have the same price in all locations. Absolute PPP compares the price of a basket of similar goods between countries, asks if the law of one price is correct on average. In practice, even if the law of one price held for every good in two economies, absolute PPP might not hold because the weights (consumption patterns) of the various goods in the two economies may not be the same.
Relative PPP: change in the exchange rate depends on the inflation rates in the two countries. In its approximate form, the difference in inflation rates is equal to the expected depreciation (appreciation) of the currency. The country with the higher inflation should see its currency depreciate. The formal equation for relative PPP is as follows: S (X/Y)
S 1 S S t X t
, if t 1, % S
X Y /
S 1 S Y
Because there is no true arbitrage available to force the PPP relation to hold, violations of the relative PPP relation in the short run are common. The evidence suggests that the relative form of PPP holds approximately in the long run.
Ex-Ante Version of PPP
The ex-ante version of purchasing power parity is the same as relative purchasing power parity except that it uses expected inflation instead of actual inflation.
1 t e
X t e Y
S E S
The International Parity Relationships Combined
IRP 1 r
1 r S y
Foreign exchange Fisher expectations relation
1 I x
Several observations can be made from the relationships among the various parity relationships:
Covered interest parity holds by arbitrage. If forward rates are unbiased predictors of future spot rates, uncovered interest rate parity also holds (and vice versa). Interest rate differentials should mirror inflation differentials. This holds true if the international Fisher relation holds. If that is true, we can also use inflation differentials to forecast future exchange rates
— which is the premise of the ex-ante version of PPP By combining relative purchasing power parity with the international Fisher relation we get the uncovered interest rate parity.As stated earlier, uncovered interest rate parity and PPP are not bound by arbitrage and seldom work over the short and medium terms. Similarly, the forward rate is not an unbiased predictor of future spot rate. However, PPP holds over reasonably long time horizons. If relative PPP holds at any point in time, the real exchange rate would be constant--called the equilibrium real exchange rate. However, since relative PPP seldom holds over the short term, the real exchange rate fluctuates around this mean-reverting equilibrium value.
Assess the long-run fair value of an exchange rate
Macroeconomic balance approach. Estimates how much current exchange rates must adjust to equalize a country’s expected current account imbalance and that country’s sustainable current account imbalance.
External sustainability approach. Estimates how much current exchange rates must adjust to force a country’s external debt (asset) relative to GDP towards its sustainable level. Reduced-form econometric model approach. Estimates the equilibrium path of exchange rate movements based on patterns in several key macroeconomic variables, such as trade balance, net foreign asset/liability, and relative productivity.
Balance-of-payments accounts Current Account measures the exchange of goods, the exchange of services, the exchange of investment income, and unilateral transfer (gifts to and from other nations) Financial Account (also known as the capital account) measures the flow of funds for debt and equity investment into and out of the country, including direct investment made by companies; portfolio investments in equity, bonds, and other securities; and other investments and liabilities such as deposits or borrowing with foreign banks.
Official reserve account transactions are those made from the reserves held by the official monetary authorities of the country. Normally the official reserve account balance does not change significantly from year to year.
Capital flows tend to be the dominant factor influencing exchange rates in