A bond with default risk will always have a ________ risk premium, and higher default risk will ________ it:

Question

BlackTom AI · Accepted Answer

Default risk means investors require extra yield above the risk‑free rate to compensate for the chance of loss, so a risky bond carries a positive risk premium that rises with greater default risk.

1) Relevant concepts
- Risk premium (or credit spread) is the extra yield over the risk‑free rate demanded by investors for bearing credit/default risk.
- Expected loss from default = probability of default × loss given default (1 − recovery rate). Lenders require compensation for this expected loss plus a premium for uncertainty and liquidity.

2) Step‑by‑step reasoning
- Let r_f be the risk‑free rate. A bond with default risk must offer yield r = r_f + RP, where RP is the risk premium.
- Since RP compensates for expected/default losses and uncertainty, RP > 0 whenever there is any nonzero probability of default.
- If the probability of default or the expected loss given default increases, the expected loss term rises. To keep investors indifferent, the bond’s yield must rise, which means RP increases (credit spread widens).

3) (No numerical calculation required) If you did use numbers: suppose r_f = 2%, probability of default p = 1%, loss given default = 50%, expected loss = 0.5% → RP must at least cover 0.5% plus additional compensation, so RP > 0. If p rises to 2%, expected loss = 1% → RP must increase.

4) Why the correct answer is correct
- A positive risk premium is necessary to compensate for default risk; higher default risk increases expected losses and risk, therefore raising the required premium.

5) Why the other options are incorrect
- a and b (negative risk premium) are wrong because investors never pay extra for risk—risky bonds pay more, not less, than risk‑free bonds.
- d (positive; lower) is wrong because higher default risk does not lower compensation; it increases it.

Conclusion: The correct choice is c. positive; raise.

A bond with default risk will always have a risk premium, and higher default risk will it:Single choice

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A bond with default risk will always have a ________ risk premium, and higher default risk will ________ it:Single choice