Financial Risk Manager Part 1

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An analyst has attempted to get some insight into the relationship between the return on stock A (R_A,t) and the return on the Nasdaq Composite index (R_NC,t). The analyst gathers historical data and comes up with the following estimates:

Expected mean return for A: 10%
Annual mean return for Nasdaq Composite: 6%
Annual volatility for Nasdaq Composite: 15%
Covariance between the returns of A and Nasdaq Composite: 5%

The analyst formulates the following regression model using the data: $R_{A,t} = \alpha + \beta R_{NC,t} + \epsilon_t$

Using the ordinary least squares technique, which of the following models will the analyst obtain?

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NNikitesh

Last updated: February 2, 2026 at 10:22

$R_{A,t} = -0.03333 + 2.2222 R_{NC,t} + \epsilon_t$

$R_{A,t} = -0.05 + 2.2222 R_{NC,t} + \epsilon_t$

$R_{A,t} = 2.2222 + 0.06 R_{NC,t} + \epsilon_t$

$R_{A,t} = 1.80 - 0.05 R_{NC,t} + \epsilon_t$

Explanation:

The regression coefficients for a model specified by $Y = \hat{\alpha} + \hat{\beta} X + \varepsilon$ , where $\varepsilon$ represents the error term, are obtained using the formula:

$\hat{\beta} = \frac{\text{Cov}(X, Y)}{\text{Var}(X)} = \frac{0.05}{0.15^2} = 2.2222$

$\hat{\alpha} = E(Y) - \hat{\beta} E(X) = 0.1 - 2.2222(0.06) = -0.03333$

Therefore, the correct regression model is: $R_{A,t} = -0.03333 + 2.2222 R_{NC,t} + \epsilon_t$

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