Chapter 20 Supervisory reserves and capital requirements (2)

Question 1

Describe what we mean by ‘market consistent valuation’? (3)

Answer 1

A market consistent valuation

is often referred to as a fair valuation which can be used to set reserves
with assets being valued at market value
theoretically the price someone would charge for taking responsibility for liability, in a market in which such liabilities are freely traded

Question 2

Describe how the investment return assumption would be determined for a market-consistent valuation of the liabiltiies (4)

Answer 2

1. Would be based on the risk-free rate, irrespective of the type of asset actually held.
2. This risk-free rate may be based on government bond yields, or on swap rates (if there’s a sufficiently deep and liquid market for these).
3. A deduction may be made for credit risk, as appropriate.
4. Credit might be taken for the illiquidity premium in corporate bond yields, provided the liabilities for which the rates are to be used
   are long term,
   and have reasonably predictable duration,
   and for which matching assets can be held to maturity (eg immediate annuties)

Question 3

Explain what’s meant by ‘illiquidity premium’ in context of corporate bond yields (5)

Answer 3

Illiquidity premium

May be possible to derive market consistent disc rate from corporate bonds
Compared to government bonds, corporate bonds
higher default probability
less marketable (hence, less liquid), => prices more volatile => problem if bonds need to be sold before redemption
usually have higher bond yields due to higher default risk and lower liquidity
illiquidity premium is portion of higher return due to illiquidity

Question 4

Solvency capital requirements:

What do we mean by solvency capital requirements? (2)

Give 2 broad areas of risk where solvency capital can protect policyholders (2)

How might the level of solvency capital required by regulation be specified? (2)

Answer 4

Solvency capital requirements refers to:

the usual that insurer supervisory bodies impose which requires insurers to maintain at least a specified level of solvency capital (i.e. capital to display solvency
can be viewed as an additional level of protection
Solvency capital requirements can protect polichyholders against:

reserve being underestimated, ie adverse future experience relative to reserving assumptions.
a drop in asset values (including individual asset defaults).
Level of solvency capital may be

specified as formula eg 3% of reserves to cover fall in asset value, and 0.3% of sum at risk to cover adverse mortality
based on a risk based measure, such as VaR (Value at Risk)

Question 5

Solvency capital requirements: relationship between reserves & solvency capital requirements

Answer 5

in some countrires, reserves are set up on a relatively realistic basis (relatively small margins from expected values), but with requirement for substantial level of solvency capital determined using risk-based capital techniques.
in other countries, reserves are set up on a relativesly prudent basis (relatively large margins), but with relativesly small solvency capital requirement, which isn’t specifically related to the risks borned by the company.

Question 6

Solvency capital requirements: Value at Risk approach

What is the VaR approach to deriving solvency capital required by an insurer? (2)

Answer 6

VaR approach is

risk-based solvency capital requirement approach, normally expressed as a min required confidence level over a defined period (eg 99.5% over 1 year)
Under VaR approach, amount of capital needed:
set min required confidene level, eg 99.5%, over a given defined eriod, eg 1 year => assets won’t exceed liabilities over 1 year, with 99.5% confidence
eg VaR of R10 mil over next year with 99.5% confidencec=> only 0.5% expected probability of loss higher than R10 mil over next year

Question 7

Solvency capital requirements: Value at Risk approach

Outline the Value at Risk (VaR) approach to dervicing the risk-based solvency capital required by an insurance company.

Answer 7

• Supervisory balance sheet subject to stress tests:
  supervisory balance sheet=>often market consistent for this approach type
  conduct stress tests/shocks on supervisory balance sheet for each risk factor separately, at defined confidence level, over the defined period.
  eg calculate R100mil capital required to cover mortality mortality risk
  each stress test involves projecting the company’s future assets and liabilities, based on the actual liabiltiies and assets currently held.
  for each risk factor, amount of capital needed at the present time, in excess of its liabilities due to stress test, is calculated to ensure that assets exceed liabitlities at the end of the defined period with the required probability.
  alternatively, determine single shock scenario with 99.5% confidence which involved simultaneously shocking mortality, expenses, investment return, withdrawals, etc => currently too computationally difficult, so seperate stress test used instead
• Aggregate capital requirement
  for individual stress tests done, combine capital required over all risk factors, allowing appropriately for interactions, eg via correlation matrix
  aggregate capital requirement…
  = sqrt[ SumOveri( SumOverj (Corr(i,j) * Cap(i) * Cap(j))) ]
  where Cap(i) is the capital requirement under risk i and Corr(i,j) is the correlation between risks i and j
  under extreme event condition being tested, correlations may differ from those observed under normal conditions=> copulas may also be use
  Additional capital may be needed across individual risks to cover any
  non-linearity (1% increase in shock <> 1% change in cap required)
  non-seperability (events happen together > if happen seperately)

Question 8

passive vs active valuation

Answer 8

A passive valuation approach is relatively insensitive to changes in market conditions and has
a valuation basis which is updated relatively infrequently.
An active approach is based more closely on market conditions, with the assumptions being
updated on a frequent basis.
Passive approaches tend to be easier to implement, involve less subjectivity and result in
relatively stable profit emergence. Active approaches are more informative in terms of
understanding the impact of market conditions.

Question 8

In summary, the ‘cost of capital’ method for determining the additional risk margin is as follows:

Answer 8

 firstly project the required capital at each future time period (ie the amount required in
excess of the projected liabilities)
 multiply the projected capital amounts by the cost of capital
 discount using market-consistent discount rates to give the overall risk margin

Question 9

(ii) How the choice of bonds would affect the discount rate used for the liabilities

Answer 9

In a market-consistent valuation, the discount rate would usually be the risk-free rate obtainable
on government bonds regardless of the choice of assets. [½]
However, an illiquidity premium can sometimes be included in the discount rate used for the
liabilities to take credit for the illiquidity premium in the yield on the assets held. [½]
A higher discount rate will lead to a lower value of the liabilities, … [½]
… and so a better solvency position. [½]
If the insurer has chosen to hold the government bonds, it will not be able to include an illiquidity
premium in its discount rate. [½]
If the insurer has chosen to hold either of the corporate bonds, then it may be able to include an
illiquidity premium, … [½]
… if this is permitted by regulation / legislation. [½]
It is only generally appropriate to include an illiquidity premium for long-term, predictable
liabilities … [½]
… which will be the case here if the insurer has a large enough portfolio to remove random
fluctuations from the experience. [½]
The corporate bonds have similar yields overall, however, they are made up quite differently: [½]
 the multinational company’s bonds have a high risk of default, but are very marketable /
liquid, … [½]
… so the majority of the yield margin (above the government bond yield) will reflect the
default risk [½]
 the small private company’s bonds have a lower risk of default, but are very unmarketable
/ illiquid, … [½]
… so the majority of the yield margin (above the government bond yield) will reflect the
illiquidity risk. [½]
Therefore, if the insurer held the multinational company’s bonds, then the scope for including an
illiquidity premium would be small, … [½]
… whereas if the insurer held the small private company’s bonds, then a significant allowance may
be made in the discount rate for illiquidity. [½]