Quantification of financial risk (parity relationships and value at risk)

Welcome to Your Guide on Quantifying Financial Risk!

In the world of F3 Financial Strategy, we don’t just say "things might go wrong"—we want to know how much they might go wrong and why. This chapter is all about putting numbers to the risks we face, specifically regarding exchange rates and potential losses. Don't worry if you aren't a math whiz; we will break these concepts down step-by-step so you can approach your exam with confidence!

Part 1: Parity Relationships – Predicting the Future

Have you ever wondered why exchange rates move? Parity relationships are economic theories that help us calculate what a future exchange rate "should" be based on things like inflation and interest rates. While they aren't perfect in the real world, they are essential tools for financial managers to estimate future costs and revenues.

1. Purchasing Power Parity (PPP)

The Core Idea: PPP says that in the long run, the exchange rate between two currencies should adjust so that a basket of goods costs the same in both countries. If a loaf of bread is expensive in the UK but cheap in the USA, the exchange rate should move to balance that out.

The Connection: PPP links exchange rates to inflation rates.

The Formula:
\( S_1 = S_0 \times \frac{1 + i_c}{1 + i_b} \)
Where:
- \( S_1 \) = Expected future spot rate
- \( S_0 \) = Current spot rate
- \( i_c \) = Inflation rate in the counter/overseas country
- \( i_b \) = Inflation rate in the base/home country

A Quick Tip: Always remember "Country C over Country B" (Counter over Base). If the inflation is higher in the foreign country, their currency will usually weaken against yours.

2. Interest Rate Parity (IRP)

The Core Idea: This theory suggests that the difference between the spot exchange rate and the forward exchange rate is caused by the difference in interest rates between two countries. It prevents "arbitrage" (making free money by moving cash between banks in different countries).

The Connection: IRP links exchange rates to interest rates.

The Formula:
\( F_0 = S_0 \times \frac{1 + r_c}{1 + r_b} \)
Where:
- \( F_0 \) = Forward rate
- \( S_0 \) = Current spot rate
- \( r_c \) = Interest rate in the counter/overseas country
- \( r_b \) = Interest rate in the base/home country

Did you know? IRP is generally considered more accurate for short-term predictions (Forward rates) than PPP is for long-term predictions, because interest rates are known today, while future inflation is just a guess!

3. The International Fisher Effect (IFE)

The Core Idea: This ties everything together. It suggests that differences in nominal interest rates between countries reflect differences in expected inflation. If a country offers a very high interest rate, it’s usually because they expect high inflation, which will eventually devalue their currency.

Quick Review of Parity:
• PPP = Uses Inflation to predict future Spot rates.
• IRP = Uses Interest rates to predict Forward rates.
• Fisher Effect = High interest rates usually mean high inflation is coming.

Common Mistake to Avoid: Don't mix up the currencies! If the exchange rate is given as \$/£, then £ is the base (1 unit) and \$ is the counter. Always put the interest/inflation of the "$" on top of the formula!

Part 2: Value at Risk (VaR)

Now that we’ve looked at why rates move, let’s look at Value at Risk (VaR). This is a favorite topic for CIMA examiners. VaR answers one simple question: "What is the maximum amount I could lose, with a certain level of confidence, over a specific time?"

The Three Components of VaR

To calculate VaR, you need three pieces of information:
\n1. Confidence Level: Usually 95% or 99%.
\n2. Time Horizon: One day, one week, or one month.
\n3. The Amount at Risk: The total value of your investment or position.

Understanding the "Confidence Level"

If a company has a 95% VaR of \$1 million over one day, it means:
• We are 95% confident that our loss will not exceed \$1 million tomorrow.
\n• There is a 5% chance (1 in 20 days) that our loss will be more than \$1 million.

The Calculation Formula

For the exam, you will usually use the standard deviation (volatility) to find VaR:
\( \text{VaR} = \text{Value of Position} \times \text{Standard Deviation} \times Z\text{-score} \)

What is a Z-score? It’s just a number from a statistical table that matches your confidence level. You don't need to memorize the whole table, but these two are very common:
• 95% confidence = 1.65 standard deviations (Z = 1.65)
• 99% confidence = 2.33 standard deviations (Z = 2.33)

Step-by-Step VaR Example

Scenario: You hold a portfolio worth \$10,000,000. The daily standard deviation is 2%. What is the 95% VaR for one day?
\nStep 1: Identify your Z-score. For 95%, it is 1.65.
\nStep 2: Multiply the Portfolio Value by the Standard Deviation.
\n\( \$10,000,000 \times 0.02 = \$200,000 \)
\nStep 3: Multiply that result by the Z-score.
\n\( \$200,000 \times 1.65 = \$330,000 \)
\nConclusion: There is a 95% chance that the daily loss will not exceed \$330,000.

Changing the Time Horizon

If the exam gives you a daily standard deviation but asks for a 10-day VaR, you cannot just multiply by 10! Risk doesn't grow in a straight line.
The Rule: To scale VaR over time, multiply the daily VaR by the square root of time (\( \sqrt{T} \)).
Example: 10-day VaR = Daily VaR \( \times \sqrt{10} \).

Advantages and Limitations of VaR

Pros:
• It gives a single, easy-to-understand dollar figure for risk.
• It allows managers to compare risks across different departments (e.g., FX risk vs. Stock risk).

Cons:
• It doesn't tell you the "worst-case" scenario. It only tells you what happens 95% of the time. In that "5% failure zone," the loss could be much, much higher!
• It relies on historical data, and the future doesn't always look like the past (black swan events).

Key Takeaway for VaR: It’s a great tool for "normal" market conditions, but it can be dangerous if management ignores what happens in the extreme 1% or 5% of cases.

Summary and Final Tips

Quantifying risk is about turning uncertainty into something manageable.
• Use PPP and IRP to estimate where exchange rates are heading based on inflation and interest.
• Use VaR to set limits on how much your business is willing to lose in a day or month.

Exam Strategy: When you see a VaR question, check the confidence level first to find your Z-score, then check if you need to scale the time using the "square root of time" rule. For Parity questions, always double-check which currency is the "base" and which is the "counter" before plugging numbers into the fraction!

Keep going! Financial Strategy can be complex, but once you master these formulas, you'll be able to quantify any risk that comes your way.