残差项

问题如下：

An analyst is estimating the sensitivity of the return of stock A to different macroeconomic factors. He prepares the following estimates for the factor betas:

β (industrial Production)=1.3, β (interest Rate)=-0.75

Under baseline expectations, with industrial production growth of 3% and an interest rate of 1.5%, the expected return for Stock A is estimated to be 5%.

The economic research department is forecasting an acceleration of economic activity for the following year, with GDP forecast to grow 4.2% and interest rates increasing 25 basis points to 1.75%.

What return of Stock A can be expected for next year according to this forecast?

选项：

A.

4.8%

B.

6.4%

C.

6.8%

D.

7.8%

解释：

The expected return for Stock A equals the expected return for the stock under the baseline scenario, plus the impact of "shocks", or excess returns of, both factors. Since the baseline scenario incorporates 3% industrial production growth and a 1.5% interest rate, the "shocks" are 1.2% for the GDP factor and 0.25% for the interest rate factor.

Therefore the expected return for the new scenario

=Baseline scenario expected return +β_{Industrial Production}×Industrial Production shock +β_{Interest Rate} ×Interest Rate shock

=5%+(1.3×1.2%)+（-0.75×0.25%）=6.37%

股票A的预期收益等于该股票在基线情景下的预期收益，加上“冲击”的影响，或两个因素的超额收益。
由于基线情景包含3%的工业生产增长和1.5%的利率，因此GDP因素的“冲击”为1.2%，利率因素的“冲击”为0.25%。
因此，新方案的预期回报=基线情景预期收益+β工业Production×Industrial生产冲击+β利率×Interest利率冲击
= 5% +(1.3×1.2%)+(-0.75)×0.25% = 6.37%