Final answer:
The present value of the derivative's expected cash inflow is $2.29, and the outflow is -$1.52 when discounted at the risk-free rate of 5%. Assessing the systematic risk of the derivative compared to the underlying security requires more information on market conditions and derivatives structure.
Step-by-step explanation:
Valuing a Derivative Security
To determine the value of a derivative security, we must examine its expected cash flows and adjust them for risk and the time value of money. In the scenario provided, the derivative will result in a cash inflow of $2.40 if the underlying security increases to $15, and it will require a $1.60 cash outflow if the security decreases to $10. Given that the current risk-free rate is 5%, we can calculate the present value of these future cash flows.
First, calculate the expected cash flow of the derivative:
If the security price increases: Expected inflow is $2.40
If the security price decreases: Expected outflow is -$1.60
To calculate the present value, we use the formula PV = CF / (1 + r)^t, where PV is the present value, CF is the cash flow, r is the risk-free rate, and t is the time period. Thus, we have:
PV of inflow = $2.40 / (1 + 0.05)^1 = $2.29
PV of outflow = -$1.60 / (1 + 0.05)^1 = -$1.52
The risk-free asset moves with the economy and has a beta of 1. Since the derivative's payoff is directly tied to the price of the underlying security, we must consider that its risk could be different. In general, a derivative might have more systematic risk (beta risk) if its cash flows are more volatile than the underlying asset. Without further information on the underlying security's beta or the derivative's correlation with the market, we cannot determine the systematic risk of the derivative relative to the security. More information on market conditions and the derivative's design would be needed.