在無風險報酬為6%、市場報酬率為15%下，有一beta為1.2，股價為$25且在下一年度會發$1股利的股票。今有一投資人認為此股在年底時股價將上升為$28，則他會採取何項措施：A.市場上股價被低估，所以應買入B.市場上股價被高估，所以應放空C.市場上股價被低估，所以應放空D.市場上股價被高估，所以應買入

Break Down the Problem

1. Identify the components of the problem:

   • 無風險報酬 (Risk-free rate) = 6%
   • 市場報酬率 (Market return rate) = 15%
   • Beta = 1.2
   • 現股價 (Current stock price) = $25
   • 下一年度股利 (Dividend next year) = $1
   • 投資人預測未來股價 (Investor's predicted future price) = $28

2. Determine if the stock is undervalued or overvalued based on investor's expectations vs. intrinsic value.

Relevant Concepts

1. CAPM (Capital Asset Pricing Model) to determine the expected return: $E(R) = R_f + \beta \times (E(R_m) - R_f)$ Where:

   • $E(R)$ = Expected return on the stock
   • $R_f$ = Risk-free rate (6%)
   • $E(R_m)$ = Expected market return (15%)
   • $\beta$ = Beta of the stock (1.2)

2. Calculate the intrinsic value of the stock using the dividend discount model (DDM): $P_0 = \frac{D_1}{E(R) - g}$ Assuming growth rate $g = 0$ for simplicity in this case.

Analysis and Detail

1. Calculate Expected Return: $E(R) = 0.06 + 1.2 \times (0.15 - 0.06) = 0.06 + 1.2 \times 0.09 = 0.06 + 0.108 = 0.168 \quad (or \, 16.8\%)$

2. Determine the intrinsic value using DDM: Since we assume no growth ($g = 0$): $P_0 = \frac{1}{0.168} \approx 5.95$

3. Comparison with current and future price:

   • Current Price: $25
   • Predicted Future Price: $28
   • Based on intrinsic value, the stock price appears high at $25, but the predicted future price suggests it may rise.

Verify and Summarize

• Since the predicted future price ($28) is higher than the current price ($25), it suggests the stock may be undervalued.
• However, the intrinsic value of approximately $5.95 indicates a premium on the stock price.

Final Answer

Given these calculations, the investor would reason as follows:

• The true intrinsic value suggests the stock is overvalued at $25.
• The projected $28 price suggests potential growth.

Thus, the correct answer is: A.市場上股價被低估，所以應買入 (The market price is undervalued, so should buy).