Identify and examine the considerations that shape which investment securities a bank selects.
The idea
A bank does not simply buy the highest yield. The investment portfolio mainly serves as a secondary liquidity reserve, a source of income, a diversifier of loan risk and collateral for pledging. Selection factors are credit quality, marketability, maturity and interest rate risk, call or prepayment risk, tax status, pledging requirements and regulatory liquidity treatment. Marketability is how fast and cheaply a security sells near market value. Expected loss is the probability of default times the loss given default, so compare yields net of it. Tax-exempt yields are compared with taxable ones through the tax-equivalent yield, written TEY. TEY = tax-exempt yield ÷ (1 − tax rate). Pledged securities are not available for sale, so liquidity should be measured on unpledged holdings at market value. The common error is ranking securities by promised yield instead of risk-adjusted, after-tax yield.
Formulas
Tax-equivalent yield
TEY = tax-exempt yield ÷ (1 − t)
- tax-exempt yield
- the yield on the tax-exempt security
- t
- the investor's marginal tax rate
Compares a tax-exempt bond with taxable ones. Multiplying by (1 − t) gives an after-tax yield, the wrong direction.
Yield net of expected credit loss
Expected yield = promised yield − PD × LGD
- promised yield
- the yield if every payment is made
- PD
- the probability of default
- LGD
- the loss given default, one minus the recovery rate
Ranks securities on risk-adjusted rather than promised yield. Using the recovery rate in place of LGD is the trap.
A practice question
In selecting investment securities, the marketability of a security refers to:
- how quickly and cheaply it can be sold close to its current market value. - correct
- the probability that the issuer will pay interest and principal on time.Why not: Describes credit risk, a separate selection factor from marketability.
- how soon the principal is repaid to the holder.Why not: Describes maturity, not marketability.
- the yield remaining after the bank's income taxes.Why not: Describes after-tax yield, which is a tax consideration rather than marketability.
Marketability (liquidity) is the ease of selling at little price concession; it depends on issue size, dealer activity and quality. It is distinct from credit risk, maturity and tax treatment.
A harder one
A bank with a 21% marginal tax rate compares a municipal bond yielding 3.60% (interest fully tax-exempt, no disallowed funding cost) with taxable bonds. The tax-equivalent yield on the municipal bond is closest to:
- 4.36%Why not: Adds the tax rate: 3.60% x (1 + 0.21). Tax-equivalent yield divides by (1 - t).
- 4.56% - correct
- 2.84%Why not: Computes the after-tax yield, 3.60% x (1 - 0.21), the wrong direction for a tax-equivalent yield.
- 5.54%Why not: Uses the former 35% corporate tax rate: 3.60% / 0.65, not the stated 21%.
Tax-equivalent yield = tax-exempt yield / (1 - tax rate) = 3.60% / 0.79 = 4.56%. A taxable bond must yield more than this to beat the municipal on an after-tax basis.
The hardest tier
A bank is considering a corporate bond with a promised yield of 5.90%, a one-year probability of default of 2.0% and a loss given default of 55%. Expected loss is probability of default x loss given default, and the bank reduces the promised yield by it. The expected yield net of expected credit loss is closest to:
- 5.00%Why not: Uses the recovery rate of 45% instead of loss given default 55%, giving expected loss of 0.90%.
- 3.90%Why not: Subtracts the default probability of 2.0% alone, ignoring that part of the exposure is recovered.
- 4.80% - correct
- 5.78%Why not: Multiplies the promised yield by (1 - 2.0%), applying default probability to the yield rather than the loss.
Expected loss = 2.0% x 55% = 1.10%. Expected yield = 5.90% - 1.10% = 4.80%. Comparing securities on promised yield overstates the return from credit risk.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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