CFA Level 1 - Interest Rate Caps and Floors

Interest Rate Cap An interest rate cap is actually a series of European interest call options (called caplets), with a particular interest rate, each of which expire on the date the floating loan rate will be reset. At each interest payment date the holder decides whether to exercise or let that particular option expire. In an interest rate cap, the seller agrees to compensate the buyer for the amount by which an underlying short-term rate exceeds a specified rate on a series of dates during the life of the contract. Interest rate caps are used often by borrowers in order to hedge against floating rate risk.

Formula 15.5

(Current market rate – Cap Rate) x principal x (# days to maturity/360)

Interest Rate FloorFloors are similar to caps in that they consist of a series of European interest put options (called caplets) with a particular interest rate, each of which expire on the date the floating loan rate will be reset. In an interest rate floor, the seller agrees to compensate the buyer for a rate falling below the specified rate during the contract period. A collar is a combination of a long (short) cap and short (long) floor, struck at different rates. The difference occurs in that on each date the writer pays the holder if the reference rate drops below the floor. Lenders often use this method to hedge against falling interest rates.

The cash paid to the holder is as follows:

Formula 15.6

(Floor rate – Current market rate) x principal x (# days to maturity/360)

Value at Risk - VaR

VaR is commonly used by banks, security firms and companies that are involved in trading energy and other commodities. VaR is able to measure risk while it happens and is an important consideration when firms make trading or hedging decisions.

In financial mathematics and financial risk management, Value at Risk (VaR) is a widely used risk

measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, probability and

time horizon, VaR is defined as a threshold value such that the probability that the mark-to-market loss on

the portfolio over the given time horizon exceeds this value (assuming normal markets and no trading in

the portfolio) is the given probability level.

For example, if a portfolio of stocks has a one-day 95% VaR of $1 million, there is a 0.05 probability that

the portfolio will fall in value by more than $1 million over a one day period, assuming markets are

normal and there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1

day in 20. A loss which exceeds the VaR threshold is termed a “VaR break.”

The 5% Value at Risk of a hypothetical profit-and-loss probability density function

VaR has five main uses in finance: risk management, risk measurement, financial control, financial

reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well.

Capital at Risk

Usually a measure of credit risk. Although maximum possible losses are sometimes brought up in

discussions of capital at risk, the predominant approach is to measure capital at risk as a function of the

probability distribution of economic loss. The probability distribution of economic loss is, in turn, a

function of the distributions and correlations of potential replacement cost, default, and recovery. What

may be described as the worst case scenario is usually a 95 or 90 percentile case, not the worst outcome

imaginable.

A measure of worst-case losses in excess of the average that is used in banking to calculate both capital

requirements and certain performance measures, such as risk-adjusted return on capital (RAROC). It is

usually based on the value-at-risk methodology.

Risk adjusted return on capital

Risk adjusted return on capital (RAROC) is a risk-based profitability measurement framework for

analysing risk-adjusted financial performance and providing a consistent view of profitability across

businesses. The concept was developed by Bankers Trust and principal designer Dan Borge in the late

1970s. Note, however, that more and more Return on risk Adjusted Capital (RORAC) is used as a

measure, whereby the risk adjustment of Capital is based on the capital adequacy guidelines as outlined

by the Basel Committee, currently Basel II.

Basic formula

RAROC = (Expected Return)/(Economic Capital) or

RAROC = (Expected Return)/(Value at risk)

Broadly speaking, in business enterprises, risk is traded off against benefit. RAROC is defined as the ratio

of risk adjusted return to economic capital. The economic capital is the amount of money which is needed

to secure the survival in a worst case scenario, it is a buffer against expected shocks in market values.

Economic capital is a function of market risk, credit risk, and operational risk, and is often calculated by

VaR. This use of capital based on risk improves the capital allocation across different functional areas of

banks, insurance companies, or any business in which capital is placed at risk for an expected return

above the risk-free rate.

RAROC system allocates capital for 2 basic reasons:

Risk management

Performance evaluation

For risk management purposes, the main goal of allocating capital to individual business units is to

determine the bank's optimal capital structure—that is economic capital allocation is closely correlated

with individual business risk. As a performance evaluation tool, it allows banks to assign capital to

business units based on the economic value added of each unit.

Capital Adequacy Ratio - CAR

What Does Capital Adequacy Ratio - CAR Mean?

A measure of a bank's capital. It is expressed as a percentage of a bank's risk weighted credit exposures.

Capital adequacy ratios ("CAR") are a measure of the amount of a bank's core capital expressed as

a percentage of its assets weighted credit exposures.

Capital adequacy ratio is defined as:

TIER 1 CAPITAL -A)Equity Capital, B) Disclosed Reserves

TIER 2 CAPITAL -A)Undisclosed Reserves, B)General Loss reserves, C)Subordinate Term Debts

where Risk can either be weighted assets ( ) or the respective national regulator's minimum

total capital requirement. If using risk weighted assets,

 ≥ 10%.

The percent threshold varies from bank to bank (10% in this case, a common requirement for regulators

conforming to the Basel Accords) is set by the national banking regulator of different countries.

Two types of capital are measured: tier one capital (T1 above), which can absorb losses without

a bank being required to cease trading, and tier two capital (T2 above), which can absorb losses in the

event of a winding-up and so provides a lesser degree of protection to depositors.

Also known as "Capital to Risk Weighted Assets Ratio (CRAR)."

Capital adequacy ratio is the ratio which determines the capacity of the bank in terms of meeting the time

liabilities and other risks such as credit risk, operational risk, etc. In the most simple formulation, a bank's

capital is the "cushion" for potential losses, which protects the bank's depositors or other lenders. Banking

regulators in most countries define and monitor CAR to protect depositors, thereby maintaining

confidence in the banking system.

CAR is similar to leverage; in the most basic formulation, it is comparable to the inverse of debt-to-equity

leverage formulations (although CAR uses equity over assets instead of debt-to-equity; since assets are by

definition equal to debt plus equity, a transformation is required). Unlike traditional leverage, however,

CAR recognizes that assets can have different levels of risk.

Capital Adequacy Ratio - CAR

This ratio is used to protect depositors and promote the stability and efficiency of financial systems

around the world.

Two types of capital are measured: tier one capital, which can absorb losses without a bank being

required to cease trading, and tier two capital, which can absorb losses in the event of a winding-up and

so provides a lesser degree of protection to depositors.

Basel 1

From 1965 to 1981 there were about eight bank failures (or bankruptcies) in the United States. Bank

failures were particularly prominent during the '80s, a time which is usually referred to as the "savings

and loan crisis." Banks throughout the world were lending extensively, while countries' external

indebtedness was growing at an unsustainable rate. (For related reading, see Analyzing A Bank's

Financial Statements.)

As a result, the potential for the bankruptcy of the major international banks because grew as a result of

low security. In order to prevent this risk, the Basel Committee on Banking Supervision, comprised of

central banks and supervisory authorities of 10 countries, met in 1987 in Basel, Switzerland.

The Purpose of Basel I

In 1988, the Basel I Capital Accord was created. The general purpose was to:

1. Strengthen the stability of international banking system.

2. Set up a fair and a consistent international banking system in order to decrease competitive inequality

among international banks.

The basic achievement of Basel I has been to define bank capital and the so-called bank capital ratio. In

order to set up a minimum risk-based capital adequacy applying to all banks and governments in the

world, a general definition of capital was required. Indeed, before this international agreement, there was

no single definition of bank capital. The first step of the agreement was thus to define it.

Two-Tiered Capital

Basel I defines capital based on two tiers:

1. Tier 1 (Core Capital): Tier 1 capital includes stock issues (or share holders equity) and declared

reserves, such as loan loss reserves set aside to cushion future losses or for smoothing out income

variations.

2. Tier 2 (Supplementary Capital): Tier 2 capital includes all other capital such as gains on investment

assets, long-term debt with maturity greater than five years and hidden reserves (i.e. excess allowance for

losses on loans and leases). However, short-term unsecured debts (or debts without guarantees), are not

included in the definition of capital.

Credit Risk is defined as the risk weighted asset (RWA) of the bank, which are banks assets weighted in

relation to their relative credit risk levels. According to Basel I, the total capital should represent at least

8% of the bank's credit risk (RWA).

Basel II

 is the second of the Basel Accords, which are recommendations on banking laws and regulations issued

by the Basel Committee on Banking Supervision. The purpose of Basel II, which was initially published

in June 2004, is to create an international standard that banking regulators can use when creating

regulations about how much capital banks need to put aside to guard against the types of financial and

operational risks banks face. Advocates of Basel II believe that such an international standard can help

protect the international financial system from the types of problems that might arise should a major bank

or a series of banks collapse. In theory, Basel II attempted to accomplish this by setting up risk and capital

management requirements designed to ensure that a bank holds capital reserves appropriate to the risk the

bank exposes itself to through its lending and investment practices. Generally speaking, these rules mean

that the greater risk to which the bank is exposed, the greater the amount of capital the bank needs to hold

to safeguard its solvency and overall economic stability.

Objective:

The final version aims at:

1. Ensuring that capital allocation is more risk sensitive;

2. Separating operational risk from credit risk, and quantifying both;

3. Attempting to align economic and regulatory capital more closely to reduce the scope

for regulatory arbitrage.

While the final accord has largely addressed the regulatory arbitrage issue, there are still areas where

regulatory capital requirements will diverge from the economic.

Basel II has largely left unchanged the question of how to actually define bank capital, which diverges

from accounting equity in important respects. The Basel I definition, as modified up to the present,

remains in place.