Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Deep dive into the quiz with AI chat providers.

We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.

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 goes ahead and 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?

Exam-Like

Community

TTanishq

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

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

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

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

Explanation:

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

Where:

$\text{Cov}(X,Y) = 0.05$ (covariance between returns)
$\text{Var}(X) = (0.15)^2 = 0.0225$ (variance of Nasdaq Composite returns)
$E(Y) = 0.10$ (expected mean return for stock A)
$E(X) = 0.06$ (annual mean return for Nasdaq Composite)

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

Powered ByGPT-5.2

Comments

Loading comments...