ICAG_CPD_FinModel_FX

ICA GHANA2015 CPD WORKSHOPS

FINANCIAL MODELLING

BUSINESS VALUATION

ESTIMATION OF FOREIGN EXCHANGE RATES

FACILITATOR: ANTHONY ESSEL-ANDERSON, CA

FACILITATOR INFORMTION

ANTHONY ESSEL-ANDERSON

Lecturer in Accounting and Finance, Ashesi University College

Management Consultant, EsselAnderson Consult

E-mail: [email protected] [email protected]: 024 280 6155 020 836 3329

3 Feb 2015 Prepared by A. Essel-Anderson 2

mailto:[email protected]

mailto:[email protected]

FX Forecasting

Foreign exchange plays important role in international trade

Importance of FX forecasting

Forecasting based on technical analysis

Forecasting based on fundamental analysis

Forecasting based on international parity conditions


Objectives


• Appreciate the theory that underlies forex rate determination in an uncontrolled exchange rate regime

• Model the following • Estimation of FX rate using absolute PPP

• Estimation of FX rate using relative PPP

• Estimation of FX rate using forward parity

• Estimation of FX rate using interest rate parity

Technical analysis

• Look for trends in exchange rates and Forex trading volumes that predict future exchange rate

• Past exchange rate and volume data are used to forecast short-term trends in currency rates.

• Effective for short-term forecasts.


Fundamental analysis

• Look for the link between exchange rate behaviour and economic fundamentals.

• Macro-economic data is used to forecast long-term trends in currency rates.

• Effective for long-term forecasts.


International parity conditions

• Relative PPP

• Forward Parity

• Interest Rate Parity


The Law of One Price

The Law of One Price

• Purchasing Power Parity


In the absence of transaction costs and official trade barriers, identical goods will have the same price in different markets when the prices are expressed in the same currency.

When the law is true within the bounds of transaction costs, an identical asset has the same value regardless of the currency in which its value is measured.

Purchasing Power Parity (PPP)

3 Feb 2015 9Prepared by A. Essel-Anderson

• Meaning• It is an economic theory that estimates the amount of adjustment needed

on the exchange rate between currencies for the exchange to be equivalent to each currency's purchasing power.

• Applications• Used to estimate relative value of different currencies.

• Used to estimate the direction of exchange rate in the long run.

Absolute PPP and Relative PPP


• Absolute PPP• In equilibrium, a basket of goods should cost the same in two

different countries once you take the exchange rate into account.

• Relative PPP• Predicts a relationship between the inflation rates (i.e. general

price level) of two countries over a specified period and the movement in the exchange rate between their currencies over the same period.

Absolute PPP Exchange Rate

• Absolute PPP connects FX rates to price levels.

• FX rates are determined by price levels.

• The quotient of the prices of identical commodity in two different currencies is the PPP spot rate:

• The price of the commodity in one currency is the product of the price of the commodity in the other community and the PPP spot rate:


Activity 1.1: Absolute PPP FX Rate

A Toshiba Ultrabook is selling at USD1,100 in the United States. The price of the Ultrabook is GHS3,600in Ghana.

Does Absolute PPP hold if the current spot rate is GHS3.2013?

If not, what should be the spot rate?


When Absolute PPP does not hold


• When absolute PPP does not hold, you may pursue a profitable arbitrage by buying the commodity from one country and selling in the other.

• Consider transaction costs when taking this decision.

The Relative Version of PPP


• The relative version of PPP connects change in FX rate to change in price level (i.e. inflation).

• Change in FX rate is determined by inflation.

• PPP refers to relative PPP unless it is stated otherwise.

• PPP change in FX rate is the inflation differential between the countries in question:

• Where • πA = inflation rate in Country A

• πB = inflation rate in Country B

• T = forecast period in years

∆ FX rate =1 + πA

1 + πB

T

− 1


Forecasting FX Rate based on Relative PPP

Next

Relative PPP FX Forecasts: The underlying Principle


If Relative PPP holds, percentage change in FX rate equalises percentage

change in price levels (inflation)

On the assumption that PPP holds, FX rates may be forecasted as under

E Std/f = S0

d/f 1 + πd

1 + πf

TE(St

d/f)

S0d/f

=1 + πd

1 + πf

T

Using Relative PPP to Estimate FX Rate

Look for current spot rate for the currency pair, Sd/f

0

Estimate annual rate of inflation for the respective countries from CPI data, πd and πf.

Estimate expected change in the FX rate for various forecast periods using the estimated inflation rates.

Multiply the expected change in FX rate (i.e. inflation differential by the current spot to obtain forecast FX rate).

Think about the Relative PPP FX equation


E Std/f = S0

d/f 1 + πd

1 + πf

T

Activity 1.2: Estimating Inflation Rates and PPP Change in FX Rate


• Let’s use the historical CPI for Ghana and the United States to estimate annual inflation rate (refer to accompanying Excel Workbook).

• Let’s estimate the percentage change in cedi/dollar exchange rate for various periods on the assumption that relative PPP holds.

Step 1: Compute annual CPI for Ghana and USA

Step 2: Compute annual inflation rates in Ghana and USA

Step 3: Estimate expected inflation in Ghana and USA

Step 4: Estimate percentage change in the USDGHS rate

Estimating Expected Inflation


• Ghana CPI historical data may be obtained from the website of Ghana Statistical Service or Bank of Ghana

• CPI historical data for Developed economies, such as US, Japan, EU area, Canada, Australia, may be obtained from RateInflation(http://www.rateinflation.com/consumer-price-index/euro-area-historical-cpi)

• Inflation rate is determined from CPI data as under:

Inflation rate, π =CPItCPIt−1

− 1

Getting CPI Data from BoG Web

Open Home page > Statistics > Monetary Time Series Data

Click on the series you want in the Available Series array

Click on the >> button next to Available Series array

Select frequency and start and end years

Finally, click on the Submit Query button


Computing Annual Inflation Rates

Find annual CPI by averaging monthly CPI.

Compute annual inflation using equation below:


Estimating Expected Inflation

Break-even Inflation Approach The Fisher Equation Approach


• Look for real yield on an inflation-linked risk-free security.

• Look for nominal yield on a fixed-rate risk-free security.

• The break-even inflation is the nominal yield on Fixed-rate security minus the real rate on inflation-linked security.

• The Fisher equation with periodic compounding:• 1+ i = (1 + r) x (1 + π)

• Where

• i = nominal interest rate

• r = real interest rate

• π = expected inflation rate

• Expected inflation is estimated as• π =(1 + i)/(1 + r) - 1

Estimating Future Inflation: A Crude Measure

We may use an arithmetic average of historical inflation as a rough measure of future inflation.


π = t=1N INFLtN

Estimating PPP Change in FX Rate

Using the expected annual inflation rates in Ghana and USA, we estimate the PPP change in USDGHS rate as under


∆ FX rate =1 + πA

1 + πB

T

− 1

What-if Analysis on Forecast FX Rate

You may use Data Table to see the effect of changing two variables on the forecast FX rate formula. You may use 1-dimensional or 2-dimensional Table

You may use Scenario Manager to study the effect of changing many different variables on the result.


You can get the What-If Analysis tools in the Data Tools group under the Data tab. With Excel 2007 or later, click on the Data tab and then select What-If Analysis in the Data Toolsgroup.

Using the 1-dimensional Data Table

We can use the 1-dimensional Data Table to project USDGHS exchange rate for various periods.

To create the 1-dimensional Data Table, we may arrange the various values for period in either a column or row.

Having arrange the values in a column or row, we compute the Forecast FX rate formula result using a base case.

Select the array of cells containing the various periods and the formula estimate, and then select Data Table from the What-if analysis options in the Data Tools group under the Data tab


Using the 2-dimensional Data Table

We can use the 2-dimensional Data Table to project USDGHS exchange rate for varied values for inflation in GH and US.

To create the 2-dimensional Data Table, we may arrange the GH inflation rates in a row and the US inflation rates in a column.

Having arrange the inflation values, we compute the Forecast FX rate formula result using a base case.

Select the array of cells containing the various periods and the formula estimate, and then select Data Table from the What-if analysis options in the Data Tools group under the Data tab


Using the Scenario Manager

The Scenario Manager in Exceluses values in user-defined scenarios to produce varied results of a formula.

We may create a Base-case, Best-case, and Worst-case scenarios, each with a set of values for GHinflation, US inflation, and current spot rate, and save them in Excel.

We then run the Scenario Manager data tool to produce scenario reports.


Creating the Scenarios On the Data tab, in the Data Tools group, click

What-If Analysis drop-down arrow, and then click Scenario Manager.

When the Scenario Manager dialog box appears, click Add to add a new scenario.

In the Scenario name box, type a name for the scenario, say Best_case.

In the Changing cells box, enter the references for the cells that you want to specify in your scenario.

In the Scenario Values dialog box, type the values that you want to use in the changing cells for this scenario (i.e. type the values for the Best-case, 12% for GH_inflation, 3% for US_inflation, and 2.9855 for Spot_ rate.

Click OK to create the scenario


Generating the Scenario Summary Report

See how the changing cells will affect the USDGHS rate forecast results, we must command the Scenario Manager to produce a scenario summary report:

Click Summary … in the Scenario Managerdialog box.

When the Scenario Summary dialog box appears, fill in the result cells. Result cells refers to the cells containing the results of the formula (in this case, the cell containing the results of the Forecast USDGHS rate formula).

Click OK, and Excel produces a scenario summary in a new worksheet.


Report of Scenario Analysis of Forecast USDGHS Rate



Forecasting FX Rate based on Forward Parity

Next

Forward Parity


• Forward exchange rate quoted by FX Dealers may serve as predictor of expected spot exchange rate• E[St

d/f] = Ftd/f

• Where

• Std/f is spot rate in t periods from now

• Ftd/f is forward rate for a contract maturing in t periods from now

Activity 1.4: Forecasting Future FX Rate using Forward Parity


• Let’s consider the forward rate points in the screenshot of FXStreet.com.

• The current spot rates are USD1.1356/EUR bid and USD1.1358/USD ask.

• Let’s compute the forward exchange rate for the various periods and use the forward exchange rates to predict future spot rates.

Computing Forward FX Rates

Observe the forward points in the screenshot of FXStreet.com

Forward points a typically expressed in basis points (1/10,000 of the reference currency).

To determine forward rate, divide forward points by 10,000 and add the result to the current spot rate.

On the assumption that dealers’ prediction is right, the future spot rate is set to the forward rates.



Forecasting FX Rate based on Interest Rate Parity

Next

Interest Rate Parity

If interest rate parity holds, forward premium equalises

interest rate differential

Based on interest rate parity, future exchange rate is

forecasted as under


Ftd/f

S0=1 + id

1 + if

T

E(Std/f) = S0

1 + id

1 + if

T

Activity 1.5: Forecasting FX Rate using Interest Rate Parity


• Let’s consider nominal interest rates on Government of Ghana and U.S. Federal Government Treasury bills.

• Let’s use the nominal interest rates for the same maturity to estimate interest rate differentials for various periods.

• Supposing current spot ask rate is GHS3.2145/USD, let’s forecast the USDGHS rate for a year from now.

• Nominal rates on GoG Treasury bills may be obtained from the Bank of Ghana website (www.bog.gov.gh).

• Nominal rates on U.S. Federal Government Treasury bills may be obtained from the U.S. Department of the Treasury website (www.treasury.gov)

http://www.bog.gov.gh/

http://www.treasury.gov/

Using Interest Rate Differential to Forecast Future FX Rate

Step 1: Compute the GH and US interest rate differential for t years from now

Step 2: Multiply current spot rate by the interest rate differential computed in Step 1. The result is the Forecast future USDGHSrate t years from now


Forecasting Future FX Rate for Various Forecast Period using the Data Table tool


ICAG_CPD_FinModel_FX

Documents

Transcript of ICAG_CPD_FinModel_FX