15 Technical and Quantitative Aspects of Risk Management

D. Folkerts-Landau, and Marcel Cassard
Published Date:
July 2000
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Erol Hakanoglu

In this paper, I will try to focus on some of the more technical and quantitative aspects of risk management. What will be covered can apply equally to assets or liabilities. In particular, we will focus on some of the classic issues and questions of how we determine maturity profile, fixed-to-floating ratios, and currency composition, but also on some of the other issues raised previously such as the proper measures of risk. Along the way, we also address problems facing some sovereign borrowers—many of which probably do not have the luxury to go along with the “theorem” Mike Dooley suggested: issuing at the longest maturity in the domestic currency. Unfortunately, it is seldom the case that emerging market sovereigns have the luxury to be able to borrow for 30 years in their domestic markets in significant amounts.

In general terms, strategic liability and/or asset managers need to set an appropriately long horizon for themselves, and come up with some sort of optimization framework that will give them a sense of what the best performance of a portfolio relative to a benchmark is. If we were to follow the results of such an optimization and rebalance our portfolio accordingly, say by either issuing new debt or swapping existing debt to change its currency, or maturity, or fixed-floating composition, we should have a portfolio that reflects our preferences, or utility, more effectively than before.

Optimization is something that can be both an art and a science. Whenever one rebalances a portfolio, the assumptions being made are going to be important. Hence, one needs to come up with a strategy that, even on contrarian scenarios, guarantees that one still ends up better off than not following the recommended course of action. With a rebalancing strategy that is robust enough, one should be better off in the contrarian scenarios as well. This should be the conditions of optimality, not the ones that give a better utility only if one’s views about the future are correct. Since it is not obvious that one will be able to satisfy such stringent conditions each time one tries to optimize, perhaps sometimes one should not rebalance at all unless this “robustness” criteria has been satisfied. I believe this is the right way to think about asset, liability, and risk management in general.

Development of a Framework

The Goldman Sachs Multicurrency Asset-Liability Management Model uses Monte Carlo simulations to characterize the probable future behavior of asset or liability portfolios. The Monte Carlo simulation approach necessitates the preparation of an elaborate probabilistic framework to model the behavior of economic and financial variables. Here are the steps we take:

  • (1) Choosing appropriate stochastic processes to model the variables involved. Most market variables, such as interest rates and exchange rates, are often modeled as lognormal, and their defining parameters are estimated from historical data and current market prices. However, sometimes it might be necessary to use other less traditional stochastic processes such as Poisson jumps.

  • (2) Construction of a historical variance/covariance matrix for all variables. This includes discussion of which periods to include in this estimation and what weights to use for each period.

  • (3) Selection of an appropriate short-term horizon. This is for tactical analysis and an appropriate long-term horizon for strategic analysis.

  • (4) Making appropriate “rollover” assumptions. This is done for all the various classes of instruments in the liability portfolio.

  • (5) Deciding on the list of financial strategies, such as:

    • fixed and floating rate new debt issues;

    • refunding of callable debt or implementation of strategies, such as selling swaptions or warrants to monetize the embedded options of callable bonds;

    • repurchasing of noncallable outstanding debt;

    • interest rate swaps;

    • cross-currency swaps;

    • forward and futures contracts;

    • options on interest rates, exchange rates, indices or commodities, structured notes, and swaps;

    • inflation-linked debt issues;

    • foreign exchange-linked debt issues; and

    • customized hedging instruments.

  • (6) Determination of future cash flows—resulting from all instruments in the current debt and asset portfolios and all the rebalancing strategies considered.


The Goldman Sachs Multicurrency Asset-Liability Model uses Monte Carlo simulations extensively. The methodology includes generating thousands of realistic scenarios for future exchange rates, interest rates, and other relevant variables, and computation of cash flows resulting from individual instruments in the portfolio as well as the revenues and expenses of the sovereign. This computation might also involve the simulation of the decision-making process of the portfolio manager in cases such as deciding when to refund callable bonds.

Given a particular scenario, the cash-flow set of each instrument is determined by the market conditions over that scenario. For example, the cash flows of a domestic floating rate note depend on the relevant domestic interest rate, while the cash flows for a foreign bond depend on the relevant exchange rate. We can then proceed with measurement of the net present value (NPV) and average annual cost/return of each instrument under each scenario. Following steps include construction of the probability distribution of the average annual cost/return of each instrument, and measurement of the expected cost/return as the mean of the distribution. Then we construct the probability distribution of the average annual cost/return of the overall portfolio over the long term, as well as the short term, by aggregating the results for individual instruments. We conclude simulations by determining the impact of incrementally changing the currency composition, maturity profile, or fixed/floating mix of the asset and liability portfolio.

Risk Measurement

A detailed discussion of risk measurement methods is an important step in the liability management process. Goldman Sachs believes that the risk measurement methods that are to be developed for the sovereign should be:

  • quantitative;

  • objective;

  • comprehensive;

  • isolating the actions of the sovereign from market moves beyond the control of the sovereign; and

  • analytically straightforward to implement.

The conventional measure of risk for a liability portfolio is the standard deviation of the cost distribution. More sophisticated measures take into account the fact that not all uncertainty is unfavorable: high interest cost scenarios are risky while low interest cost scenarios are not. Such a one-sided approach will allow us to separate negative uncertainty from positive uncertainty. One-sided risk measures can be used to take into account asymmetric utility functions that place greater weight on the penalty of potential interest cost increases than on the benefits of equivalent potential interest cost savings.

One-sided risk can be defined in a variety of ways. The probability of exceeding a fixed cost level (derived from expected cost of the current portfolio under forward rates or budgetary considerations of the sovereign) could be used as a performance criterion. However, a fixed cost level is too restrictive to incorporate essential information about various sources of interest rate, exchange rate, or liquidity risk. It is not flexible enough to reflect the sovereign’s debt management objectives and capital markets constraints.

A systematic way to quantify risk in a sophisticated, reliable, and flexible manner is to measure risk against a benchmark portfolio that is constructed to take into account various market and non-market constraints and concerns of the portfolio manager. After the development of such a benchmark portfolio, risk can be defined as the underperformance of the portfolio relative to the benchmark.

The most important sources of risk that a sovereign borrower needs to address can be summarized as follows:

  • liquidity risk;

  • interest rate risk;

  • cash-flow uncertainty;

  • rollover risk;

  • mark-to-market risk;

  • exchange rate risk; and

  • credit risk.

The Goldman Sachs Asset-Liability Management Model is capable of measuring risk from a cash-flow perspective and from a mark-to-market perspective. In the past, asset managers have traditionally focused on mark-to-market uncertainty, while liability managers have focused on cash-flow uncertainty. These two approaches often lead to different results. For example, long-term fixed rate bonds are risk-less from a cash-flow perspective, but risky from a mark-to-market perspective. Floating rate notes, on the other hand, exhibit the opposite characteristic. Goldman Sachs believes that it is essential to consider both forms of risk simultaneously.

The budgetary targets of the sovereign will be thoroughly examined during the risk measurement and benchmark selection parts of the Asset-Liability Management analysis. We will also analyze the methodology by which the sovereign determines these targets and evaluate their advantages and disadvantages as performance measurement tools.

Selection of a Strategic Benchmark

Selection of a strategic benchmark constitutes the pillar of the Goldman Sachs Asset-Liability Management approach. We believe that the success of any risk management effort is heavily dependent on the appropriateness of the underlying performance benchmark. A benchmark portfolio is a convenient way to aggregate various market exposures as well as many factors constraining the portfolio choice. We will work on both the liability portfolio and the liquid reserve portfolio during the benchmark selection process.

The risk of a liability portfolio can be measured in a variety of ways. One common approach is to determine the expected cost of the existing portfolio over a chosen horizon under forward rates and to use the probability of underperforming this fixed cost level as a performance criterion. An alternative method is to use the probability of the cost of debt being above an absolute amount dictated by budgetary considerations. However, such fixed rate benchmarks do not properly take into account relevant information from sources other than the immediate debt portfolio, which could affect the interest rate, exchange rate, commodity price, and liquidity risk of the sovereign. For example, trade and capital flows, liquid asset and reserve portfolios, tax revenues, policy guidelines, and macroeconomic variables can all be important factors affecting portfolio choice and risk considerations.

A simple way to conceptualize the strategic benchmark portfolio is to treat it as a default long-term portfolio designed to have a currency composition, maturity profile, and fixed/floating mix that reflects the riskless position for the sovereign in the long run. This concept can be expanded to incorporate the borrowing goals, capital markets objectives, and policy constraints of the sovereign.

The factors that will most likely impact the currency composition of the benchmark portfolio are:

  • historical statistical relationships between exchange rates;

  • relative bond market sizes in various currencies;

  • new issue spreads of the sovereign in these markets; and

  • the impact of foreign exchange flows on the economic activity level and the tax revenues of the sovereign.

The factors that are most likely to impact the maturity profile of the benchmark portfolio are:

  • revenue and expense forecasts of the sovereign over the next few years;

  • repurchase or tender plans;

  • liquidity concerns of the sovereign; and

  • spreading of cash flows over the years in order to smooth refinancing exposure.

The factors that are most likely to impact the fixed/floating mix of the benchmark portfolio are:

  • targeted interest expense levels of the sovereign from the budget;

  • the interest rate views of the sovereign;

  • relationship among tax revenues, business cycles, and interest rates;

  • historical cost of fixed versus floating rate debt; and

  • relative risk of foreign fixed and floating issues in comparison to domestic debt.

Other factors that need to be considered during the development of the benchmark portfolio are:

  • continuing accessibility of various markets considered;

  • the need to maintain high-volume debt issues to achieve market liquidity, efficiency, and long-term cost benefits such as facilitating future repurchases or tenders;

  • the relationship between commodity prices, exchange rates, and domestic macroeconomic variables;

  • accounting guidelines;

  • policy constraints limiting the use of certain financial instruments; and

  • mark-to-market rules for derivative instruments.

A benchmark portfolio that is created by taking into account all the issues mentioned above is a fairly close approximation of the “ideal” long-term portfolio of the sovereign. It will represent a minimum risk position for the sovereign, since it will be constructed to take into account all the various market exposures, long-term objectives, and market and policy constraints the sovereign is operating under. As the benchmark portfolio will be selected to represent primarily the strategic preferences of the sovereign, tactical deviations from the benchmark portfolio can be undertaken periodically to take advantage of market opportunities and to reduce cost.

Using a strategic benchmark for risk management has several advantages. It creates a structure that ensures that future strategies conform to the strategic risk management objectives of the sovereign. It provides a straightforward method of combining many of the diverse factors affecting the portfolio choices of the sovereign. It allows the sovereign to set limits on risk tolerance levels and creates a mechanism to enforce these levels. Once the benchmark is in place, portfolios can be optimized within well-defined parameters and their performance can be judged on objective criteria.

Formulation of Strategies

A primary objective of the liability management study is to develop strategies to enhance the cost/risk profile of the liability portfolio. We list below some examples from previous sovereign liability management studies to demonstrate our approach toward formulation of strategies. We are able to add many more to this list after studying the specific information provided to us by the sovereign. These may include:

  • Calculation of the impact of changing the maturity profile, fixed/floating ratio, and currency composition on the cost and risk of the liability portfolio.

  • Identifying the effect of buying caps and floors on the probability of falling short of budget targets.

  • Examining ways to reduce the expected cost of hedging instruments through knock-in and knock-out features.

  • Performing a refunding efficiency analysis for callable bonds in the liability portfolio to determine whether any call options are sufficiently in the money to justify calling the bond.

  • Exploring alternative strategies such as selling swaptions or warrants to monetize the value in the embedded options of the callable bonds.

  • Designing new issue strategies to replace called bonds or to fulfill new funding needs of the sovereign.

  • Exploring the possibility of linking debt payments to inflation and foreign exchange rate levels.

  • Structuring of custom-tailored hedging instruments that precisely hedge market exposures of the sovereign.

  • Exploration of derivative structures that hedge multiple exposures together in a cost-effective way.


The objective of the cost/risk optimization section of the Goldman Sachs Asset-Liability Management Model is to determine to what extent the cost/risk profile of the asset and liability portfolios can be improved and to select the most effective transactions to do so. We define a portfolio to be optimal if it is the lowest-cost portfolio for a given level of risk or, equivalently, if it is the lowest-risk portfolio for a given level of cost.

The efficient frontier is the set of optimal portfolios. A portfolio that is not on the efficient frontier is not optimal because there exists a portfolio with both lower cost and lower risk. The slope of the efficient frontier quantifies the cost/risk trade-off associated with different strategies.

The choice of which optimal portfolio to select depends ultimately on the borrower’s risk tolerance. A borrower with a high-risk tolerance will prefer a strategy that minimizes cost, while a borrower with a low-risk tolerance will prefer a strategy that minimizes risk.

Over the course of the liability management analysis, we will perform a rebalancing optimization—to find the best strategies to change the composition of the debt portfolio without changing its size. Then we will perform a new issue optimization, to find the best ways to increase the size of the debt portfolio. Finally, we will perform a refunding efficiency analysis to determine optimal ways to reduce the size of the debt portfolio.

Sensitivity Analysis

The sensitivity analysis allows us to test potential restructuring strategies against various potential market moves and ensure that they perform within acceptable risk parameters.

A sensitivity analysis can be performed in a discrete form or in a simulation framework. A discrete sensitivity analysis measures the performance of a strategy under an elaborately defined future path of market variables. A simulation-based sensitivity analysis involves repeating the scenario generation, cash-flow simulation, and portfolio evaluation steps described earlier under alternative scenarios, where different expected future levels for exchange rates and interest rates are used. The Goldman Sachs Multicurrency Asset-Liability Management Model has the capability to perform both types of sensitivity analyses.

There are many ways of constructing sensitivity scenarios. One common choice is using shock scenarios, where interest and exchange rates are subjected to parallel one or two standard deviation moves up and down from their base-case levels. Another is to create contrarian scenarios, which represent the opposite views from the base-case scenario with respect to implied forward rates or specific forecasts.

In addition to the scenarios described above, a robust sensitivity analysis should focus on adverse scenarios that are picked specifically to determine how poorly certain strategies perform under extremely unfavorable market conditions. This can be done by performing another set of Monte Carlo simulations that are adjusted specifically to assign more probability to adverse market moves, or by simulating the behavior of potential strategies through actual past observations to determine the worst possible historical outcomes. Goldman Sachs recommends only strategies that either outperform the existing portfolio or perform within acceptable risk parameters under all sensitivity scenarios.

The Goldman Sachs approach to sensitivity analysis is not limited to calculating the sensitivity of the results to changes in market variables. We also determine the effects of changing the composition of the strategic benchmark or relaxing some of the policy guidelines.

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