1Insurance companies in a developed country have investment portfolios of long dated

corporate bonds to match their liabilities. The regulatory regime requires that these

insurers must invest only in bonds with credit ratings of BBB- or higher ( Investment

Grade'' bonds). When the credit rating of a bond is downgraded to BB+ or lower

( Sub-Investment Grade'), or defaults, the insurer is required to immediately sell the

downgraded bond and buy an Investment Grade bond of their choice.

(i) Explain why the value of a bond may fall when it is downgraded to

Sub-Investment Grade. [2]

(ii) Explain how the regulatory regime described above will help reduce credit

risk. [2]

(iii) Outline the limitations of using credit ratings in the above regulatory regime to

reduce credit risk. [4]

An insurer has a large portfolio of corporate bonds, including a $100m exposure to a

15-year bond that currently has a credit rating of BBB ( Big Bond'). The insurer is

considering hedging the costs associated with Big Bond being downgraded to a rating

of BB. The insurer has been offered the following standard Credit Default Swap

(CDS) from a bank with the following terms:

underlying = Big Bond

notional of CDS = $100m

term of CDS = 3 years

CDS spread = 2%, which is paid at the end of each year, contingent on Big Bond

not defaulting during that period (i.e. there is no accrual payment on default).

The insurer assumes:

a recovery rate of 40% .

the probability of Big Bond defaulting during a year conditional on no earlier

default is 4% .

defaults occur at the end of the year.

risk-free interest rates are assumed to be 0% at all terms.

(iv) Demonstrate that the value of the CDS to the insurer is $1.4m. [4]

The insurer has calculated that if Big Bond immediately downgrades to a credit rating

of BB:

the cost of selling the downgraded Big Bond and buying an appropriate

Investment Grade bond would be $30m.

the value of the CDS would increase from $1.4m to $8.2m based on an assumed

probability of Big Bond defaulting during a year conditional on no earlier default

of 8% when it is rated BB.

(v) Calculate the required notional of the CDS for the insurer to hedge its $30m

costs associated with an immediate Big Bond downgrade. [2]

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'SP6 A2020-7 PLEASE TURN OVER

(vi) Determine, without performing any further calculations, whether the required

notional calculated in part (v) to hedge the fixed $30m cost would increase,

decrease or remain approximately unchanged in each of the following separate

scenarios:

(a) The term of the CDS is increased from three years to 10 years.

(b) The insurer assumes a recovery rate of 50% (rather than 40%).

[3]

(vii) Suggest practical challenges associated with using the increase in value of the

CDS to fund the expected $30m costs associated with the downgrade of Big

Bond to a credit rating of BB

A defined benefits pension fund is currently underfunded and has a significant

proportion of its investment portfolio invested in equities with a current value of

20 million in the local currency.

(i) Describe the typical uses of derivatives in its investment portfolio. [4]

The pension fund is concerned about the risk of extreme falls in the equity market.

The trustees of the pension fund are considering several options to manage this risk.

(ii) Explain why reducing the equity exposure may not meet the wider objectives

of the trustees. [2]

To better manage the risk, the trustees are considering using derivatives.

(iii) Describe how put options could be used to manage the risk. [3]

The pension fund's equity investment has a similar weighted composition as the main

equity index used in the country. Its hedging strategy is to spend 0.5% of its equity

portfolio value at the start of each calendar month on buying two-month European put

options on the equity index that are 30% below the current underlying price (of the

equity index).

On the first day of the calendar month the options are purchased using the following

information:

The equity index value is 2,000.

Strike price Option price at the start of

the current trading day

Number of options traded on

the previous day (millions)

1,350 0.02 32

1,400 0.11 2

1,450 0.01 47

(iv) Demonstrate that the number of options required to implement the hedge

as detailed above is 909,091. [2]

(v) Comment on how the hedge could be implemented given the current market

conditions. [3]

The number of options as calculated in part (iv) was eventually purchased in the

market at the price shown in the table above at the start of the calendar month. At the

end of the calendar month, before the options are sold, the equity index has fallen 20%

and the implied volatility has risen to 50%.

Risk-free interest rate: 2% (continuously compounded)

Equity index dividend yield: 4% (continuously compounded)SP6 A2020-9

(vi) Demonstrate that the Black-Scholes value of the put options held

is 19,158,000. [4]

(vii) Assess the effectiveness of the hedging strategy at the end of the calendar

month. [2]