Unit study guide · NISM Series XV
Fundamentals of Risk and Return
10 questions in this unit
What this unit covers
- A stock has a beta of 1.3 relative to a broad market index. What does beta primarily measure?
- A portfolio earned 14% during a period in which the risk-free rate was 6%. The portfolio's standard deviation of returns was 10%. What was its Sharpe ratio?
- An investor adds more stocks whose company-specific return drivers are not perfectly correlated with the existing portfolio. As the portfolio becomes well diversified, which risk is most directly reduced?
- The risk-free rate is 5%, the expected market return is 12%, and a stock's beta is 1.3. Under CAPM, the stock's expected return is:
- Two risky assets have a return correlation of exactly +1. An investor combines them with positive portfolio weights. Which statement is most accurate?
- An investment gains 10% in Year 1 and loses 10% in Year 2. What is the total compounded return over the two years?
- An analyst values a company under different assumptions for revenue growth, operating margin and discount rate. What is the main purpose of this sensitivity analysis?
- An investment earns a simple holding-period return of 6% over six months. Using simple annualisation and assuming a 12-month year, the annualised return is:
- A portfolio returns 15%, the risk-free rate is 5%, and the portfolio beta is 1.25. What is its Treynor ratio?
- An analyst values a stock at ₹420 after new information materially weakens its outlook, but keeps insisting it is worth at least ₹600 mainly because ₹600 was its IPO price. Which bias is most directly illustrated?
Key ideas
From the practice bank · 1
A stock has a beta of 1.3 relative to a broad market index. What does beta primarily measure?
Beta measures systematic market sensitivity: how a security's returns tend to move relative to the market return used as the benchmark. Remember: Beta is a measure of systematic market risk, not total risk.
Hint Common mistake: Equating beta with standard deviation.
XV-021From the practice bank · 2
A portfolio earned 14% during a period in which the risk-free rate was 6%. The portfolio's standard deviation of returns was 10%. What was its Sharpe ratio?
Sharpe ratio = (Portfolio return − Risk-free rate) ÷ Standard deviation = (14% − 6%) ÷ 10% = 0.80. Remember: Sharpe ratio uses excess return over the risk-free rate divided by total volatility.
Hint Common mistake: Using the portfolio return directly without subtracting the risk-free rate.
XV-022From the practice bank · 3
An investor adds more stocks whose company-specific return drivers are not perfectly correlated with the existing portfolio. As the portfolio becomes well diversified, which risk is most directly reduced?
Diversification reduces company-specific or unsystematic risk when exposures are not perfectly correlated. Broad market or systematic risk cannot generally be diversified away simply by holding more stocks. Remember: Diversification reduces idiosyncratic risk, not the market-wide component of risk.
Hint Common mistake: Believing that enough securities make a portfolio risk-free.
XV-041From the practice bank · 4
The risk-free rate is 5%, the expected market return is 12%, and a stock's beta is 1.3. Under CAPM, the stock's expected return is:
CAPM expected return = Rf + β(Rm − Rf) = 5% + 1.3(12% − 5%) = 5% + 9.1% = 14.1%. Remember: CAPM combines the risk-free rate with beta times the market risk premium.
Hint Common mistake: Forgetting to add the risk-free rate after calculating beta × market risk premium.
XV-042From the practice bank · 5
Two risky assets have a return correlation of exactly +1. An investor combines them with positive portfolio weights. Which statement is most accurate?
With correlation of +1, the assets move perfectly together in standardized terms, so combining them does not create the risk reduction that comes from less-than-perfect correlation. With positive weights, portfolio volatility is the weighted combination implied by perfect positive correlation. Remember: The diversification benefit comes from imperfect co-movement, not merely from holding multiple assets.
Hint Common mistake: Assuming any two-asset portfolio is automatically diversified.
XV-043From the practice bank · 6
An investment gains 10% in Year 1 and loses 10% in Year 2. What is the total compounded return over the two years?
If the starting value is 100, after a 10% gain it becomes 110. A 10% loss then reduces 110 to 99. The total compounded return is therefore −1%. Equal percentage gains and losses do not cancel because the second percentage applies to a different base. Remember: Investment returns compound multiplicatively across periods.
Hint Common mistake: Adding percentage returns arithmetically when calculating multi-period wealth change.
XV-089From the practice bank · 7
An analyst values a company under different assumptions for revenue growth, operating margin and discount rate. What is the main purpose of this sensitivity analysis?
Sensitivity analysis tests how an output such as valuation responds to changes in key inputs. It helps identify which assumptions matter most and the range of plausible outcomes, but it does not eliminate uncertainty. Remember: Sensitivity analysis makes model dependence on assumptions visible.
Hint Common mistake: Presenting a single-point valuation without testing the assumptions that drive it.
XV-090From the practice bank · 8
An investment earns a simple holding-period return of 6% over six months. Using simple annualisation and assuming a 12-month year, the annualised return is:
Simple = 6% × (12 ÷ 6) = 12%. This is simple annualisation, not compounded annual growth. Remember: Know whether a question asks for simple annualisation or compounded annualisation.
Hint Common mistake: Applying a compounding formula when the question explicitly specifies simple annualisation.
XV-127From the practice bank · 9
A portfolio returns 15%, the risk-free rate is 5%, and the portfolio beta is 1.25. What is its Treynor ratio?
Treynor ratio = (Portfolio return − Risk-free rate) ÷ Beta = (15% − 5%) ÷ 1.25 = 8.0%. Remember: Treynor uses systematic risk measured by beta, unlike Sharpe which uses total volatility.
Hint Common mistake: Using standard deviation in the Treynor denominator.
XV-128From the practice bank · 10
An analyst values a stock at ₹420 after new information materially weakens its outlook, but keeps insisting it is worth at least ₹600 mainly because ₹600 was its IPO price. Which bias is most directly illustrated?
Anchoring occurs when a decision-maker relies too heavily on an initial reference point even after new information should cause a meaningful update. Remember: Reference prices can become psychologically sticky even when fundamentals change.
Hint Common mistake: Treating a historical market price as evidence of current intrinsic value.
XV-129CAGR expresses the change between a starting value and an ending value as a single constant annual rate.
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