Risk Assessment and Interest Rate Risk 3rd Ed.

Financial Strategy — Unit 7

The Open University

Publisher: The Open University, 2000, 94 pages

ISBN: 0-7492-9786-7

Keywords: Finance, MBA

Last modified: Sept. 11, 2022, 3:21 p.m.

Risk is said to come from the Arabic word risq ('anything that has been given to you (by God) and from which you draw profit') or the Latin word risicum (originally referring to challenges to seafarers, potentially with a negative outcome). The concept of risk brought foreward in the book talks about something that has an uncertain outcome possibly improving or worsening one's position. It has a probability, can be good or bad (ex credit risk, which can only be bad) and involves something changing. The question is how to assess this.

Risk mapping is one potential solution, being an aid to increase the knowledge of risk exposure within the organisation. It is both an idea and a technique. Different risks to look at might be foreign exchange or interest rate risk and actually other internal audits, aimed at potentially suggesting improvements. There are three steps in this:

  1. find involved risk categories
  2. estimate size and degree of exposure
  3. rank risks for prioritisation

You should always look back to the strategy when doing this.

Risk categories (suggestion):

  • financial: monetary changes due to balances and resource changes, e.g. gearing of different operations and he business
  • organisational: industrial relations, labour costs, skill requirements, price/quality, processes, R&D,
  • market: Market share, distribution, demand, product range
  • Environmental: STEEP

To estimate risk you can take the formula:

Expected return = Sum over all (probability of outcome * value of outcome)

Also keep in mind avoidable risk, which should only be taken if the expected return is positive. In the end, choose the options with the highest expected return.This gives you necessary conditions but not necessarily sufficient ones. There might be catastrophic outcomes attached that you need to avoid, outweighing any potential positive return. As a reminder, in the NPV valuation, you would put the risk into the discount rate. A decision tree will help in finding out about linkages between choices and their implications. At the end, after all your analysis you should be able to answer about your risks:

  • Why are you exposed
  • What is the size of the exposure
  • What are warning signs
  • What is the cost of risk
  • What are correlations of risks

Then you allocate your risk capacity, ranking your different risks. The OUBS suggests:

  • Unavoidable risk in relation to core activities
  • Risk only avoidable by ceasing non-core activities
  • Avoidable risk, core activities
  • Avoidable risk, non-core activities
  • Selectable risk

In a sense you are moving further out of the region of your core capabilities and you must link this ranking to your strategy and appetite for risk.

In the end, while you will never be able to say what your risk is, the market will give a clear indication of what it thinks. It is important to note that strategy still drives the business, while risk mapping allows you to make sure you do not overstep your stated boundaries.

The book then includes a template and some questions to ask for financial risk analysis. The template has the different stakeholder groups on the y-achsis and the different risks on the x-achsis (e.g. forex rate, interest rate, commodity price, equity&funding, …)

Interest rate risk is something that can be managed specifically and also applies for equity investors. This should first bring us to bonds. These can be said to be a securitised evidence of indebtedness. They normally have maturities between 5 and 15 years and mostly a fixed-rate or floating-rate. As it is securities, it is freely transferable. There are registered bonds, in which the issuer has a registry of who currently owns the bonds and bearer bonds, meaning that they are anonymous and whoever shows up with the paper gets the interest. Bonds normally repay the principal at the end of the period and interest once or at different times of the year. They might be quoted as Bond1 11/2 2010" being a bond with 5.5% interest maturing 2010. Bonds are normally quoted at prices in relation to 100%, meanign that a bond valued at 95 is traded at 95% of face value.


To quantify interest rate risk, you can use the measure of duration, introduced by F.R. Macaulay in 1938. In general you already have a coupon rate and mixed with the price and that coupon rate you get a yield to maturity which gives us the IRR of the bond. If the interest rates move, the fair return or YTM changes though and how much it changes depends on the sensitivty of the bond towards interest rates. This is what duration measures. If your assets equal those of your liabilities and the duration of the both are the same, then your portfolio is immunised. This method can be applied to any know series of cash flows.

The duration is actually the weighted average maturity. That means that the formula is as follows:

D= (1/Price of the bond) * (t_1 * (CF_1 / (1+r)^(t_1)) + … + t_n * (CF_n / (1+r)^(t_n)))

An easy calculation would be to calculate the present value of the cash flows of a bond over the entire timeframe. Then you multiply each of those results by the time and add that up too. Deviding the later by the former will give your the duration in years. The discount rate should be the yield to maturity of the bond(s).

The rule is:

  • The longer the duration, the higher the exposure to interest rate risk
  • If the duration is the same, the exposure is the same, independant of sequence of cash flows.

Due to compound interest, the further away a cash flow is, the more exposed it is to interest rate changes. With zero coupon bonds, duration equals maturity. You can also adapt the formula to reflect the changes in value of a portfolio with interest rate changes.

δ(P) = -D x P x 1/(1+r) x δ(r)

Interest Risk Management Instruments

For a percentage change, simply devide by P. For bigger changes this can be wrong though as it assumes a straight line relationship between price and yield, which is a curve. An immunised portfolio will be good for changes of +/- 1%, which leaves enough time to rebalance your portfolio.

There are some special instruments for interest risk control, and the ones discussed here are forward rate agreements (FRAs), interest rate futures and swaps. All these are derivatives, meaning that their price movements is derived from the movement in an underlying asset. FRAs are over-the-counter (OTC) deals while futures contracts are exchange-traded. The choice between OTC and exchange-traded derivates involves the decision of convenience against cost as OTCs can be customized to your liking, paying an extra for the privilege.

FRAs are agreements between two parties, agreeing to a fixed exchange rate in a future period of time. They will then compensate each other if it is different from the actual. A FRA would be quoted as: 'three against six months', meaning a three month period starting in three months.

Example: I get a FRA from a bank three against six months of 8%. In three months the exchange rate is at 9%, meaning that the bank will pay me back the 1% to give me the 8%. All this does not involve any loan but is simply a contract to compensate for the difference. This deal only helps me make sure that my normal borrowing conditions do not fluctuate with interest rate changes.

In the above example I would then borrow for three months but would get the difference in interest rate at the beginning of the 3 months period, meaning that it has to be discounted as payment is made at the start of the period rather than at maturity. Normally the rate of interest specified in a FRA contract is the LIBOR rate.

{(LIBOR at settlement - Contract rate) x n/365 x Contract amount} / {1+ (LIBOR at settlement x n/365)}

The company will still pay the usual spread above LIBOR in its borrowing.

The advantages of FRAs are:

  • You do not have to borrow, as this is independant of that action
  • You can reverse your FRA by taking an equal and opposite one, called off-setting. They do not eliminate each other but do cancel each other out in terms of profit and loss.
  • FRAs are tailored by banks.

Futures on interest rates and other things are another important option. They developed from forward trading, a contract to deliver a specific quantity of goods at a certain quality in the future at a certain date to a certain price. Futures are standardised forwards with specific size and settlement dates. Future contracts are not made directly but through a clearing house and your position in a futures contract you bought can be closed at once by selling the same. They are very liquid, also due to the clearing house, while forwards might not be sellable when you want to. Very few futures contracts actually reach maturity and 98%+ are closed out before settlement. If there are more futures or forwards in a market, this depends on how important and/or costly tailoring of these derivatives is. Foreign exchange trading is often done in OTC deals while interest rate trading is done in futures.

A little bit more on the clearing house is in order. In simple, each party trading via the clearing house settles their account at the end of the day to start without a profit or loss at the start of the next day. When going into a deal you normally have to deposit an initial margin and after movements in the market, a marking to market will happen which puts the account balances back in order by crediting and debiting so called variation margins. While this requires daily payments from both buyer and seller, they do not need to know each other as everything goes via the clearing house. At delivery time the futures price must equal the real spot price of the underlying goods. Due to the marking to markt, the buyer now has the money to pay for the goods, which would be his early agreed on price plus or minus his gain or loss which was in relation to the spot rate. Due to the big amounts of money that are potentially at place here, while only really working with margin amounts, clearing houses might only work with members who's credit ratings are checked. The margins are normally between 1% and 10% of the position taken.

Short term interest rate futures are normally priced as 100 minus the futures interest rate, meaning that 8% being the notional rate, a Eurodollar bond would be quoted as 92.00, shrinking to 91.00 if the interest rates on the Eurodollar bond rises to 9%. To make a profit on rising interest rates you need to sell a FRA now and buy it back later. The minimum price fluctuation is a tick, being 0.01%. Actual cash flows in selling and buying FRAs is only the payment of margins.

There are also long-term interest rate futures, based on long-term government bonds with 10 to 25 years maturity. With a future you pay to get delivery of something in x months. Futures prices are normallly linked to a given maturity and to a bond that is 'cheapest to deliver' for the maturity. So a sale of a futures contract equals the salve of the underlying CTD bond in x months.


Oh the joy of swaps. There is a single-currency (previously interest rate) and cross-currency (previously currency) swaps. The idea is that two company for example take out a loan but pay each others loan and they both are better off. 80-90% of Eurobonds are part of "bond plus swap" packages. You borrow currencies you don't need and swap them back to those that you need from somebody who has better access to them. You can also swap parts of portfolios of debt. Managing a SWAP-warehouse is a highly skilled taks, a very well-paid one, and allows for example a bank to mix and match different debt contracts in differnet SWAPs, in part or in total.

The general good idea of SWAPs is that it allows the buyer to have access to all markets and savings for the borrowers can comes from different reasons:

  • there might be name recognition attached to the corporation in question or the other party, allowing for better access to debt
  • there are differences in risk spreads and preferences in fixed and floating-rate debt for single-currency swaps.
  • different markets of debt are independent

All in all, swap contracts are complicated but they are being standardised and the minimum amounts needed for a profitable swap are going down as the market develops.

This synopsis is licensed under a Creative Commons License from the OUBS Blog.

  1. Introduction
    • 1.1 Introduction to the Block
      • Aims and objectives of the unit
  2. Risk Assessment
    • 2.1 Defining Risk
    • 2.2 Risk Mapping
      • Stage 1 Which risk categories?
      • Stage 2 Estimating risk
      • Stage 3 Allocating risk capital
    • 2.3 Assessing the Results
    • 2.4 A Template for Financial Risk Analysis
  3. Interest Rate Risk
    • 3.1 Interest Rate Risk
    • 3.2 Quantifying Interest Rate Risk
  4. Gap Analysis
    • 4.1 The Concept of Gap Analysis
    • 4.2 Gap Analysis: A Worked Example
  5. Duration
    • 5.1 So What is Wrong With ‘Maturity’?
    • 5.2 A Measure That Works
    • 5.3 Duration and Quantifying Interest Exposure
    • 5.4 Worked Example
  6. Interest Risk Management Instruments: FRAs and Futures
    • 6.1 Forward Rate Agreements
    • 6.2 Futures — Interest Rate and Others
      • Forwards and futures
      • The clearing house
      • Short-term interest rate futures
      • Long-term interest rate futures
    • 6.3 Worked Examples
  7. Interest Risk Management Instruments: Swaps
    • 7.1 Defining a Swap
      • Single-currency swap
      • Cross-currency swap
    • 7.2 How Can Swaps Save Money?
    • 7.3 Single Currency Swaps: A Worked Example
    • 7.4 Cross-Currency Swaps


Risk Assessment and Interest Rate Risk

Reviewed by Roland Buresund

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Last modified: May 21, 2007, 3:20 a.m.

MBA material, what do you expect?


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