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.
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.
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.
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.
During the credit crisis bank balance sheets became very stretched. The majority of banks’ business models had relied on continued access to liquidity and I have set out a number of reason for this below. Prior to the 2007-09 credit crisis, bank risk models generally relied on past data to act as a guide to the future. Therefore stress tests carried out by banks largely underestimated the linkage between market liquidity and funding liquidity as such a scenario had not occurred before. They also had relatively little focus on developing new stress test scenarios so were caught out by the crisis. Furthermore, banks typically treated the funding cost of transaction with a maturity of less than one year to be equal. When the fear of the crisis set in and large spreads opened up between the costs of funding within the one year period (i.e. spread between overnight lending and 3 & 6 month LIBOR) many banks models become inadequate and had to quickly adapt. Banks also did not properly account for the funding and liquidity requirements of off balance sheet vehicles. Banks had largely seen these as standalone and separate from their main business, however, during the crisis banks found themselves facing large legal and reputational risks if these vehicles were not brought back onto the bank’s own balance sheets. This left the banks even shorter of liquidity. Additionally, a number of banks had taken out liquidity lines with other private sector firms, whereby the banks were able to access liquidity from these firms on demand. They had allowed for this provision of liquidity in their models, however, it became very difficult for banks to draw on this liquidity during the crisis. Banks found that if they were seen to be drawing on liquidity from these sources they were perceived to be more vulnerable and subsequently cut off from other sources of liquidity. Basel III has looked to address the inadequacy of bank’s liquidity management through two liquidity ratios falling under pillar 1. The first of these is the Liquidity Coverage Ratio (LCR) which is designed to ensure banks hold sufficient high quality liquid assets such that they could survive and cover its net outflows over a 30 day period in a stress case scenario. The second is the Net Stable Funding Ratio which has a longer term focus and aims to encourage banks to fund their activities with stable sources of funding. Basel III also introduced additional liquidity monitoring metrics which look to address the mismatch of cash flow durations.
Firstly the pension scheme is exposed to the risk that the bank goes bankrupt and the contract becomes worthless. The pension fund would be left with a portfolio of illiquid, long-dated, less well rated corporate bonds. It may be the case that the pension scheme can sell these bonds and replace the original portfolio of bonds it had to begin with and be better off. However, in a situation where a bank has defaulted it is likely credit spreads will have widened and government yields fallen and the pension scheme would lose out and not be able to repurchase its original portfolio. One potential way to mitigate against this risk would be to invest through a pooled fund (like that run by F&C) which pools pension scheme money together and put the above trade on with a number of banks, thus diversifying the risk of that one bank. Another potential solution is to enter the trade with the bank’s less liquid portfolio being valued at a significant haircut to market value, thus improving the likelihood of being able to replace the liquid portfolio should the bank go under. Another solution would be to require collateralisation of the difference in value between the two portfolios so that the pension scheme could regain its portfolio should the bank default. Given the purpose of the trade in the first place it would be sensible to let the bank collateralise the trade with similar illiquid holdings at a haircut. To further mitigate this risk the pension scheme could employ an investment advisor to help assess the constituents of the illiquid portfolio. Ensuring the portfolio is well diversified can help the portfolio to retain value and hence minimise losses in the event of the bank going bankrupt. The trade also introduces liquidity risk for the pension scheme, while it is true pension schemes are long term investors and are unlikely to be forced liquidators of assets, it does not mean that pension schemes are void of risks posed by low liquidity. Most of the risks associated with low liquidity for a pension scheme are opportunistic ones. For example, suppose five years down the line, after having carried out the trade, interest rates move significantly and buyout conditions become favourable. The pension scheme would not be able to liquidate its assets for a year, in which time, markets may have moved again. Another example might be that the government wants to get pension schemes involved in infrastructure projects and offer a very attractive investment opportunity, again the pension scheme has its assets tied up and would miss out on this opportunity. There is little to be done to mitigate this risk as the pension scheme is effectively receiving a premium for its liquidity. Reducing the pension scheme illiquidity by, for example, shortening the notice period, would reduce the premium it was being paid. The only way to slightly reduce this risk without reducing the attractiveness of the trade for the bank is to ensure that the contract can be traded on the secondary market (i.e. if the pension scheme wants to get out within the years notice period, it could find another pension scheme to take its place in the trade). The easiest way for the pension scheme to do this is again to use a pooled fund. The low number of pooled funds currently offering this type of product improves the chances of the pension scheme finding a buyer in the secondary market.
If the trade was carried out on a sensible part of the pension scheme’s assets it is likely an accumulation of events will need to have occurred to put the pension scheme into financial difficulties (i.e. not being able to make benefit payments as they fall due). I believe the most likely scenario is that the world economy falls into recession, leading to rising default rates and widening credit spreads. Further, the bank with which the pension scheme had entered the trade with collapses. The pension scheme is left with a portfolio of illiquid corporate bonds which are trading at extremely distressed levels due to the widened credit spreads. To add to the pension scheme’ woes all the growth assets are likely to have also fallen in value, while the value of their liabilities rise as gilt yields fall. In addition to the bank defaulting and credit spreads rising as two reverse stress tests, the pension scheme could be put into trouble if it faced a large portion of members requesting transfer values. This could potentially lead to the pension scheme having to sell all its liquid assets to meet these transfer values. In the extreme case, the one year lock in period could lead to the pension scheme not having assets to sell to meet its on-going benefit outgo.
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