Trader's portfolio has 3 different stocks:

Stock A has volatility 20% and Beta 0.9.
Stock B has volatility 25% and Beta 1.1.
Stock C has volatility 30% and Beta 0.8.

Which Stock carries the lowest unsystematic risk?

Question

Trader's portfolio has 3 different stocks:

Stock A has volatility 20% and Beta 0.9. 
Stock B has volatility 25% and Beta 1.1. 
Stock C has volatility 30% and Beta 0.8.

Which Stock carries the lowest unsystematic risk?

BlackTom AI · Accepted Answer

Unsystematic variance = total variance − systematic (market) variance, so σ_e^2 = σ_i^2 − β_i^2·σ_m^2 (where σ_i is the stock’s total volatility and σ_m is market volatility). Comparing unsystematic risk therefore uses the quantities σ_i^2 − β_i^2·σ_m^2 for each stock.

1) Relevant concepts
- Total variance = (volatility)^2.
- Systematic (market) variance component for a stock = β^2 · σ_m^2.
- Unsystematic (idiosyncratic) variance = total variance − systematic variance. We can compare unsystematic variance across stocks even if σ_m is unspecified, by using algebraic expressions in σ_m^2.

2) Step-by-step setup
Let M = σ_m^2 (market variance). Compute unsystematic variance for each stock:
- Stock A: σ_A^2 − β_A^2·M = 0.20^2 − 0.9^2·M = 0.0400 − 0.8100·M
- Stock B: 0.25^2 − 1.1^2·M = 0.0625 − 1.2100·M
- Stock C: 0.30^2 − 0.8^2·M = 0.0900 − 0.6400·M

3) Intermediate algebraic comparison
Compare B − A: (0.0625 − 1.21M) − (0.04 − 0.81M) = 0.0225 − 0.40M. This is positive (B has higher unsystematic variance than A) provided M < 0.0225/0.40 = 0.05625 (i.e., σ_m < 23.75%). Typical market volatilities are well below 23.75%, so B usually has more idiosyncratic risk than A.

Compare C − A: (0.09 − 0.64M) − (0.04 − 0.81M) = 0.05 + 0.17M, which is always positive for any M ≥ 0. So C always has greater unsystematic variance than A.

4) Why the correct answer is correct
Because Stock A’s total variance less the β^2 market component produces the smallest residual (idiosyncratic) variance among the three for any realistic market variance. Numerical example with σ_m = 15% (M = 0.0225) confirms: A: 0.04 − 0.018225 = 0.021775; B: 0.0625 − 0.027225 = 0.035275; C: 0.09 − 0.0144 = 0.0756. A’s unsystematic variance (0.021775) is smallest.

5) Why other options are incorrect
- “Stock B” is incorrect because B’s higher beta and intermediate total volatility leave it with larger idiosyncratic variance than A for realistic market variances.
- “Unsystematic Risk is the same for all the stocks” is incorrect: different volatilities and betas produce different residual variances.
- “Stock C” is incorrect because C’s high total volatility yields the largest unsystematic variance.

6) Conclusion
Stock A carries the lowest unsystematic risk. This matches the provided answer: Stock A.

Trader's portfolio has 3 different stocks: Stock A has volatility 20% and Beta 0.9. Stock B has volatility 25% and Beta 1.1. Stock C has volatility 30% and Beta 0.8. Which Stock carries the lowest unsystematic risk?单项选择题

类似问题

Unique risk is also referred to as

As diversification increases, the firm-specific risk of a portfolio approaches

Which of the following statements regarding unsystematic risk is accura

Unsystematic risk:

Which type of risk is eliminated through diversification?

Below is an incomplete reaction scheme. Choose the correct major product from the following options.[Fill in the blank]

Choose which of the following statements A, B, C or D best describe the reduction of a carboxylic acid to give an aldehyde by a reducing reagent.[Fill in the blank]

Choose which of the following statements A, B, C or D best describes the self-aldol condensation reaction of acetophenone.[Fill in the blank]

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单