Solvency Risk and Credit Risk Flashcards
What is the primary financial risk faced by pension funds and insurance companies?
Interest rate risk due to mismatch between long-term liabilities and assets.
Why are pension fund liabilities highly sensitive to interest rates?
Because their duration is long, meaning small rate changes significantly impact their present value.
How does the balance sheet of a pension fund typically look?
Assets (stocks, bonds, derivatives)
Liabilities (present value of future pension payouts)
Equity = assets - liabilities
What is the funding ratio and why is it important?
The funding ratio is Market Value of Assets / Market Value of Liabilities.
It indicates whether a pension fund has enough assets to cover future obligations.
What happens to the funding ratio if interest rates decrease?
Liabilities increase more than assets, leading to a lower funding ratio.
What happens if the duration of liabilities (DL) is greater than the duration of assets (DA)?
The pension fund is exposed to interest rate risk because liabilities react more to rate changes than assets.
What are two ways to reduce interest rate risk for a pension fund?
Invest in long-duration bonds (but these may be illiquid)
Use interest rate derivatives (swaps, swaptions)
How can interest rate swaps help pension funds manage risk?
Receiver swaps (receive fixed, pay floating) increase asset duration, reducing mismatch with liabilities.
What is the formula for net duration exposure?
D = Duration of Liabilities - (Bonds / Liabilities) * Duration of Bonds - (Swap Notional / Liabilities) * Duration of Swap
What is a receiver swaption and why is it useful?
A receiver swaption is an option to enter a receiver swap. It protects against falling interest rates without forcing the fund to lock in low rates.
How does a receiver swaption hedge downside risk?
It gains value when interest rates fall, offsetting the increase in liability value.
What is the downside of using swaps for interest rate hedging?
They hedge risk but also limit upside potential if interest rates rise.
What is the impact of a 1% drop in interest rates on a pension fund with duration mismatch?
The funding ratio drops significantly since liabilities increase more than assets.
What is credit risk?
The risk that a borrower defaults on debt obligations, causing financial losses.
What are the two key aspects of credit risk?
Probability of default
Loss given default
What is the formula for expected loss in credit risk?
Expected loss = Probability of default * (1 - Recovery Rate)
What is the recovery rate in credit risk?
The fraction of the bond value recovered after default.
How do credit spreads relate to credit risk?
A higher credit spread indicates higher perceived default risk.
What do credit rating agencies do?
They assess a borrower’s creditworthiness and assign ratings.
What is the minimum rating for an investment-grade bond?
BBB (S&P/Fitch) and Baa (Moody’s)
What is the difference between real-world and risk-neutral default probabilities?
Real-World Probabilities are based on historical data, while Risk-Neutral Probabilities are derived from bond prices and credit spreads.
What are the three main ways to estimate default probabilities?
Credit ratings approach - uses historical data
Credit spreads approach - infers default probability from bond yields
Structural models (Merton Model) - uses firm value and volatility
What is Merton’s structural model?
It treats equity as a call option on the firm’s assets and default happens if assets fall below debt.
What is the key assumption behind Hull’s formula for default probability?
Lambda(T) = Credit Spread / 1- Recovery Rate
What is a Credit Default Swap (CDS)?
A derivative contract where the CDS seller compensates the buyer if the referenced bond defaults.
Who pays whom in a CDS contract?
CDS buyer (investor): pays a regular premium
CDS seller (bank/insurance): pays in case of default
What is the payout formula for a CDS?
Payout = (1 - R) * Notional amount
What happens to CDS spreads during a financial crisis?
They increase sharply as default risk rises.
How does a higher recovery rate affect CDS pricing?
Higher recovery rates –> lower CDS spreads, since expected loss is lower.
What is the hazard rate in credit risk?
The instantaneous probability of default over a short time interval.
What is the liquidity risk of derivatives used for credit hedging?
A pension fund may face margin calls if rates rise, forcing asset sales.
How does credit risk affect bond duration?
A bond with higher credit risk has a higher yield volatility, which increases duration.
Why are junk bonds riskier than investment-grade bonds?
They have higher default probabilities and lower recovery rates.
How do banks use CDS for risk management?
They buy CDS protection to hedge loan defaults.
