CAPM Expected Return & Alpha

Time Limit: 2sMemory: 256MB

Problem

The Capital Asset Pricing Model (CAPM) predicts an asset's expected return based on its systematic risk exposure to the market.

Jensen's alpha measures the excess return above the CAPM prediction — positive alpha indicates outperformance relative to the risk taken.

Given the risk-free rate $R_f$ , the asset's beta $\beta_i$ , the market return $R_m$ , and the asset's actual return $R_{\text{actual}}$ , compute the CAPM expected return and Jensen's alpha.

Input Format

Four space-separated floats: Rf beta Rm R_actual

Output Format

Two space-separated values: expected_return alpha, each to 4 decimal places.

Examples

Example 1

Input(Four space-separated floats: Rf beta Rm Ractual)

0.03 1.2 0.10 0.15

Output

0.1140 0.0360

E[R] = 0.03 + 1.2*(0.10-0.03) = 0.114. Alpha = 0.15 - 0.114 = 0.036.

Example 2

Input(Four space-separated floats: Rf beta Rm Ractual)

0.02 0.8 0.08 0.05

Output

0.0680 -0.0180

E[R] = 0.02 + 0.8*(0.08-0.02) = 0.068. Alpha = 0.05 - 0.068 = -0.018.

Constraints

•0 ≤ Rf ≤ 0.20
•-3 ≤ beta ≤ 3
•-0.50 ≤ Rm, R_actual ≤ 1.00
•Output expected return and alpha to 4 decimal places

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