The price of a one-year zero-coupon bond is less than its expected discounted value. This is because the risk penalty implicit in the call option price is inherited from the risk penalty of the one-year zero-coupon bond. The risk penalty is the additional return that investors require for holding a risky asset, and it is reflected in the price of the asset. In the case of a one-year zero-coupon bond, the price is less than its expected discounted value because the risk penalty reduces the price. This is because the expected discounted value is the present value of the expected future cash flows from the bond, discounted at the risk-free rate. However, because the bond carries risk, investors require a higher return, which is reflected in a lower price for the bond. Therefore, the price of the one-year zero-coupon bond is less than its expected discounted value.

Choice A is incorrect. The price of a one-year zero-coupon bond is not greater than its expected discounted value. This would imply that the bond is overpriced, which contradicts the efficient market hypothesis that states prices always fully reflect available information.

Choice C is incorrect. The price of a one-year zero-coupon bond being equal to its expected discounted value would suggest there's no risk premium embedded in the price, which isn't accurate as investors demand compensation for bearing risk.

Choice D is incorrect. It's not accurate to say that the price of a one-year zero-coupon bond isn't related to its expected discounted value at all. In fact, these two are closely related as the pricing of such bonds involves discounting their face values by an interest rate that reflects both time value and credit risk.

Things to Remember

• Risk penalty is the additional return that investors require for holding a risky asset.
• Efficient market hypothesis states that prices always fully reflect available information.
• Investors demand compensation for bearing risk, hence there is a risk premium embedded in asset prices.
• Pricing of zero-coupon bonds involves discounting their face values by an interest rate that reflects both time value and credit risk.