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# Actuarial Finance Advanced Enterprise Risk Management Finance Essay

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A rating-based credit model can typically be looked at as two separate parts; a credit sensitive component based on the firms rating and a non-credit sensitive part which looks at other factors which have an impact on a bond’s price. There are two primary ways for identifying these factors as described below. The first way to identify factor structures is to take known factors which are likely to impact the price of the bond and then use multivariate regression techniques to identify each bond’s exposure to the factor. These factors are commonly broken down into two categories: Fundamental factors – These are factors which are specific to each individual issuer and can be derived from a company’s annual report and accounts. For example, one factor could be the company’s price to book ratio. Economic factors – These are economic factors which are external to the company but known to affect the price of bonds. For example, these could include interest rates, exchange rates and / or commodity input prices. The second way to identify factors is through a statistical analysis. This method eliminates the need to have any prior knowledge about the factors affecting the bond’s price. The idea of the statistical analysis is to identify other predictable time series that, in aggregate, can mainly explain the historic returns of the bonds in question. These time series are then our factors and we can calculate the exposure of each bond to each factor. The most common way to do this is through a principal component analysis. As seen in lecture notes, if we assume changes in credit ratings are independent of the other factors identified above then an r rated bond can be valued as below: Where represents the cash flow of the bond at time i. The term represents the impact on the price of the credit rating has, i.e. the discounting impact of the credit spread. The represents the price of a default free zero coupon bond paying 1 at time t, given it is currently time . Here we can build in the factor structure pricing model described above.

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“Actuarial Finance Advanced Enterprise Risk Management Finance Essay”

## (b) Identify economic reasons for and against this point of view. [6 marks]

For: Corporate bond returns are largely driven by the underlying government bond yield (i.e the interest rate) of the same duration. Therefore, if the government bond yield at a particular duration rose sharply, the value of all corporate bonds at that duration would fall sharply, assuming credit spreads remained unchanged. A suitably large move in the government bond yield could result in all corporate bonds experience a bottom 1% or 5% outcome. Such correlations to a single underlying factor do not exist in equity markets. This is especially true for very long dated corporate bonds which are very sensitive to the underlying rate. The bottom 1% or 5% of outcomes for a bond is likely to be a default event or very close to default. A company defaulting is more likely to be a sign of hard economic times, than its common stock experiencing a tail event, which could easily be driven by a media event or localised disruption. In hard economic times you would expect the default rate to rise and credit spreads across the board to widen (i.e. tail events for a number of stocks). Equity returns are significantly more sensitive to a company’s short term results (i.e. quarterly earnings and profit reports) than its bonds. These results which can trigger tail events in a company’s equity are often released on different days and this observation would suggest equity markets have a lower tail dependency than bonds. Against When a company’s bond has a tail event, its common stock is also likely to have fallen significantly, i.e. a tail event of its own. Therefore a tail dependency for two bonds would also imply a tail dependency for the companies’ common stock. Equities are much more sensitive to market sentiment in the short term than bonds. A bad market reaction to a particular piece of news can cause equity markets to crash sharply and sell off. In these situations there are rarely stocks that are exempt from the sell off and hence equities display a high level of tail dependency. Two bonds which have significantly different credit ratings are likely to be exposed to different factors and hence what may cause a tail event for one bond might not for another. For example, a high yielding C rated bond will be a lot more sensitive to market sentiment than a AAA rated bond and this division of market sensitivity is much less pronounced in equity markets.

## (c) Describe how you might test this assertion statistically. [5 marks]

To test an assertion we first need to specify exactly what we want to test. We would therefore need to decide whether we are looking at the 5% or 1% tail event, what measure of tail dependence we want to look at and also which companies or markets we are talking about. We also then need to decide on what data we want to use to test the assertion. For example, we could use historic data for the specific companies or markets over the last X years. We would need to decide how many years to look at and in particular decide the relevance of major economic events and also consider if this history is likely to be a good representation of the future. Once we have decided on what data to use and collected this information we need to calculate the tail dependencies of pairs of bonds and the corresponding pairs of common stock. The tail dependence is given by Here, u is the level of tail dependence (i.e. the 1% or 5%) and the probability is calculated using the empirical CDFs or the two stocks and bonds given by the data. Once we have calculated the tail dependencies we need to check whether the hypothesis is true and also evaluate how significant the result is. For example, if the hypothesis holds in this one test but the tail dependencies are very close, there is little evidence to support the hypothesis. To further test the results we may wish to consider a longer time period, or splitting the period into a number of sub periods and seeing if the result still holds in each individual period.

## (d) Highlight types of insurance products the insurer might sell or investments the insurer might hold that would be particularly sensitive to correlations between different bonds or different equities in relatively adverse outcomes. [3 marks]

The insurer may sell trade credit insurance to other businesses that are looking to insure against the credit risk in their accounts receivable. An increase in the correlation of credit events for the insurer, especially in adverse conditions, may trigger a high number of claims and have a large negative impact on their business. The insurer may hold a number of complex investments in credit derivative products which are highly sensitive to correlations in adverse conditions. For example an n-th to default credit derivative whereby a pay-out is made if more than n credit names default within a predefined basket. The price of the long position in the derivative will rise dramatically if there is likely to be a high correlation in the tail of bond markets. If the correlation is expected to be relatively low then it is likely even if one name defaults others will not follow and the price will be lower. Other such investment products particularly affected by the correlation in the tail are iTraxx, CDOs, CDO-Squared, LSS and Quanto or diff swaps. The life insurer may also sell an insurance bond (or investment bond product) which allows investors to tax efficiently invest in an underlying investment fund. An investment fund which holds any of the above products will be exposed in the same way as the company to correlations in bond and equity markets.

## (c) Propose 3 reverse stress tests that might be used when reviewing and discussing the risks involved in such a transaction and indicate with reasons which of your proposed reverse stress tests might be the most plausible way in which a typical UK (defined benefit) pension fund might run into significant trouble with the proposed transaction. [6 marks]

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Actuarial Finance Advanced Enterprise Risk Management Finance Essay. (2017, Jun 26). Retrieved February 3, 2023 , from

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