AFIN8003 Week 11 - Sovereign Risk, Foreign Exchange Risk, and Off-Balance-Sheet Risk

Banking and Financial Intermediation

Dr. Mingze Gao

Department of Applied Finance

2024-10-16

Foreign exchange risk

FX exposure

An FI’s overall FX exposure in any given currency can be measured by the net position exposure, which is measured in local currency as

$\begin{aligned} \text{Net exposure}_i &= (\text{FX assets}_i - \text{FX liabilities}_i) + (\text{FX bought}_i - \text{FX sold}_i) \\ &=\text{Net foreign assets}_i + \text{Net FX bought}_i \end{aligned}$

where $i$ represents the $i$ th currency.

FI could match its foreign currency assets to its liabilities in a given currency and match buys and sells in its trading book in that foreign currency

reduce its foreign exchange net exposure to zero and thus avoid FX risk.

Financial holding companies can aggregate their foreign exchange exposure through their banking, insurance and funds management businesses under one umbrella

allows them to reduce their net foreign exchange exposure across all units.

FX rate volatility and FX exposure

We can measure the potential size of an FI’s FX exposure as:

$\begin{aligned} \text{Dollar loss/gains in currency } i &= \text{Net exposure in foreign currency } i \text{ measured in local currency} \\ &\times \text{Shock (volatility) to the exchange rate of local currency to foreign currency } i \end{aligned}$

Greater exposure to a foreign currency combined with greater volatility of the foreign currency implies greater daily earnings at risk (DEAR).
Reason for FX volatility: fluctuations in the demand for and supply of a country’s currency

FX rate volatility and FX exposure (cont’d)

Example

On September 8, 2024, an Australian FI has a net exposure to New Zealand dollar (NZD) of NZD$1,000,000. The exchange rate of AUD to NZD was 1.08 AUD/NZD.

It is now October 8, 2024, and the exchange rate becomes 1.10 AUD/NZD. The AUD has depreciated in value relative to the NZD. Calculate the FI’s dollar loss/gain for this shock to the AUD/NZD exchange rate.

The AUD value of the NZD position on September 8 is $\$1,000,000\times 1.08=\$1,080,000$ .
The AUD value of the NZD position on October 8 is $\$1,000,000\times 1.10=\$1,100,000$ .
The gain from the net long position in NZD is $\$1,100,000-\$1,080,000=\$20,000$ .

Or, the dollar loss/gain is

$\text{NZD}\$1,000,000 \times (1.10 - 1.08) = \text{AUD}\$20,000$ .

FX rate volatility and FX exposure (cont’d)

The FI has a €2.0 million long trading position in spot euros at the close of business on a particular day. The exchange rate is €0.80/$1, or $1.25/€, at the daily close. Looking back at the daily changes in the exchange rate of the euro to dollars for the past year, the FI finds that the volatility or standard deviation ( $\sigma$ ) of the spot exchange rate was 50 basis points (bp). What is the DEAR?

$\text{DEAR} = \text{Dollar value of position} \times \text{FX volatility}$

Dollar value of position = €2.0 x 1.25 $/€ = $2.5 million
FX volatility = 2.33 $\sigma$ = 2.33 x 0.005 = 0.01165
DEAR = $2,500,000 x 0.01165 = $29,125

Purchasing Power Parity

Nominal interest rate $R$ is basically the sum of inflation $i$ and real interest rate $r$ :

For two countries, e.g., Australia (AU) and United States (US), we have:

$\begin{aligned} R_{AU} &= i_{AU} + r_{AU} \\ R_{US} &= i_{US} + r_{US} \end{aligned}$

Assuming real interest rates are equal across countries: $r_{AU}=r_{US}$ , then

$R_{AU} - R_{US} = i_{AU} - i_{US}$

That is, the (nominal) interest rate spread between Australia and the United States represents the difference in inflation rates between the two countries.

Important

When inflation rates and/or interest rates change, foreign exchange rates (without government control) should adjust to account for relative differences in the price levels (inflation) between the two countries.

The Purchasing Power Parity (PPP) is one theory explaining how this adjustment takes place.

Purchasing Power Parity (cont’d)

Tip

The PPP says that the most important factor determining exchange rates is the price differences drive trade flows and thus demand for and supplies of currencies.

Specifically, the PPP theorem states that the change in the exchange rate between two countries’ currencies is proportional to the difference in the inflation rates in the two countries. That is:

$i_{domestic} - i_{foreign} = \frac{\Delta S_{domestic/foreign}}{S_{domestic/foreign}}$

where

$S_{domestic/foreign}$ is the spot exchange rate of the domestic currency for the foreign currency
$\Delta S_{domestic/foreign}$ is the change in the one-period spot exchange rate

Purchasing Power Parity (cont’d)

Suppose that the current spot exchange rate of Australian dollars for Chinese yuan, $S_{AUD/CNY}$ , is 0.17 (i.e. 0.17 dollars, or 17 cents is equal to 1 yuan). The price of Chinese-produced goods increases by 10 per cent (i.e. inflation in China $i_C$ , is 10 per cent), and the Australian price index increases by 4 per cent (i.e. inflation in Australia, $i_{AUS}$ , is 4 per cent). What will be the change of the exchange rate?

According to PPP:

$i_{AUS} - i_{C} = \frac{\Delta S_{AUD/CNY}}{S_{AUD/CNY}}$

So that

$0.04 - 0.1 = \frac{\Delta S_{AUD/CNY}}{0.17}$

Solving the equation, we get $\Delta S_{AUD/CNY} = −0.0102$ . Thus, it costs 1.02 cents less to receive a yuan. The Chinese yuan depreciates in value by 6 per cent against the Australian dollar as a result of its higher relative inflation rate. In other words, a 6 per cent fall in the yuan’s value translates into a new exchange rate of 0.1598 dollars per yuan.

Interest Rate Parity

To illustrate (covered) interest rate parity (IRP), let’s consider two investment strategies.

Strategy 1: Domestic Investment

You invest $1 domestically at an interest rate $r_d$ for one period.
After one period, your investment grows to $1 + r_d$ .

Strategy 2: Foreign Investment with Forward Contract

You convert $1 into foreign currency at the current spot exchange rate $S$ , which gives $1/S$ foreign currency.
You then invest the foreign currency amount in a foreign asset at the interest rate $r_f$ for one period.
After one period, this investment grows to $(1 + r_f)$ .
You lock in the forward exchange rate $F$ now to convert the foreign currency back to domestic currency after one period.

For these two strategies to have the same return (and eliminate arbitrage opportunities), the returns on both should be equivalent when the foreign investment is converted back using the forward rate. This gives us the CIRP condition:

$1 + r_d = \frac{(1 + r_f) \cdot F}{S}$

Rearranging, we can see the relation between interest rates and the forward rate:

$F = S \cdot \frac{1 + r_d}{1 + r_f}$

Interest Rate Parity (cont’d)

Assume the interest rate on Australian dollar securities at time $t$ equals 5 per cent and the interest rate on euro loans at time $t$ is 10 per cent. Further, suppose the $/€ spot exchange rate ( $S_t$ ) at time t is $0.60/€1 and the future exchange rate ( $F_t$ ) is $0.55/€1. If the spot exchange rate rises to $0.65/€1, what is the change on the forward exchange rate?

To find the change in the forward exchange rate due to a change in the spot exchange rate, we can start by using the IRP condition:

$F_t = S_t \cdot \frac{1 + r_d}{1 + r_f}$

Domestic interest rate (Australia), $r_d = 5\% = 0.05$
Foreign interest rate (Euro), $r_f = 10\% = 0.10$
Initial spot exchange rate, $S_t = 0.60$ AUD/EUR
Initial forward exchange rate, $F_t = 0.55$ AUD/EUR
New spot exchange rate, $S'_t = 0.65$ AUD/EUR

Let’s calculate the new forward rate using CIRP, then we’ll find the change in the forward rate.

Step 1: Calculate the New Forward Rate $F'_t$

$\begin{aligned} F'_t &= S'_t \cdot \frac{1 + r_d}{1 + r_f} \\ &= 0.65 \cdot \frac{1 + 0.05}{1 + 0.10} \\ &\approx 0.6205 \text{ AUD/EUR} \end{aligned}$

Step 2: Calculate the Change in the Forward Rate

Now, find the change between the new forward rate and the initial forward rate:

$\begin{aligned} \Delta F_t &= F'_t - F_t \\ &= 0.6205 - 0.55 \\ &\approx 0.0705 \text{ AUD/EUR} \end{aligned}$

The forward exchange rate increases by approximately 0.0704 AUD/EUR as a result of the rise in the spot exchange rate.

Statistical models for country risk evaluation

Most common form of country risk assessment scoring models based on economical factors

pick a set of variables that may be important in explaining restructuring probabilities
develop the scoring model

Commonly used economic ratios:

Total debt service ratio (TDSR)

$\begin{aligned} TDSR &= \frac{\text{Total debt service}}{\text{Exports}} \\ &= \frac{\text{Interest} + \text{amortisation on debt}}{\text{Exports}} \\ \end{aligned}$

A country’s exports are its primary way of generating dollars and other currencies.

The higher the ratio, the higher sovereign risk.

Note

Check data at World Bank’s DataBank.

Statistical models for country risk evaluation (cont’d)

Import ratio (IR)

$IR = \frac{\text{Total imports}}{\text{Total FX reserves}}$

Imports to meet demands - sometimes even food is a vital import - requires FX reserves.

The higher the ratio, the higher sovereign risk.

Note

In 2020, Greece’s IR was 626% while China’s IR aws 70%. Greece imported more goods and services than it had serves to pay for them.

Loan commitments

Commitment to make a loan up to a stated amount at a given interest rate in the future
Nowadays very popular, sometimes more so than spot loans
Charge up-front fee and back-end fee

The upfront fee applies on the whole commitment size and the back-end fee applies on any unused balances at the end of the period.

Example of the fees

Suppose an FI gives an one-year $10 million loan commitment to a firm with an upfront fee of 1/8% and back-end fee of 1/4%.

The upfront fee is $\$10,000,000 \times 1/8\% = \$12,500$ .

If the firm takes down only $8 million over the year, the back-end fee is $\$10,000,000\times 1/4\% = \$5,000$ .

Loan commitments (cont’d)

For a one-year loan commitment, let:

Base rate $BR=12\%$
Risk premium $\phi=2\%$
Upfront fee $f_1=1/8\%$
Back-end fee $f_2=1/4\%$
Compensating balance $b=10\%$
Reserve requirements $RR=10\%$
Average takedown rate $td=75\%$

Then, the promised return $1+k$ of the loan commitment is

$\begin{aligned} 1+k &= 1+ \frac{f_1+f_2(1-td) + (BR+\phi) td}{td - b\times td (1-RR)} \\ &= 1+ \frac{0.00125+0.0025(1-0.75) + (0.12+0.02) 0.75}{0.75 - 0.1\times 0.75 (1-0.1)} \\ &= 1.1566 \end{aligned}$

So $k=15.66\%$ .

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AFIN8003 Week 11 - Sovereign Risk, Foreign Exchange Risk, and Off-Balance-Sheet Risk Banking and Financial Intermediation Dr. Mingze Gao Department of Applied Finance 2024-10-16

AFIN8003 Week 11 - Sovereign Risk, Foreign Exchange Risk, and Off-Balance-Sheet Risk
Sovereign Risk, Foreign Exchange Risk, and Off-Balance-Sheet Risk
Introduction
Foreign exchange risk
Foreign exchange rates
Source of FX risk exposure
FX exposure
FX rate volatility and FX exposure
FX rate volatility and FX exposure (cont’d)
FX rate volatility and FX exposure (cont’d)
Interaction of interest rate, inflation, and exchange rates
Purchasing Power Parity
Purchasing Power Parity (cont’d)
Purchasing Power Parity (cont’d)
Purchasing Power Parity (cont’d)
Purchasing Power Parity (cont’d)
Interest Rate Parity
Interest Rate Parity (cont’d)
Managing FX risk
Sovereign risk
Introduction to sovereign risk
Credit risk vs sovereign risk
Forms of sovereign risk
Repudiation vs restructuring
Country risk evaluation
Statistical models for country risk evaluation
Statistical models for country risk evaluation (cont’d)
Statistical models for country risk evaluation (cont’d)
Statistical models for country risk evaluation (cont’d)
Statistical models for country risk evaluation (cont’d)
Statistical models for country risk evaluation (cont’d)
Off-balance-sheet risk
Off-balance-sheet (OBS) activities
Major types of OBS activities
Loan commitments
Loan commitments (cont’d)
Risks associated with loan commitments
Letter of credit
Risks associated with letters of credit
Derivative contract
Sale of when-issued securities
Loans sold
Role of OBS activities in reducing risk
Finally…
Suggested readings
References