Questions: Asset Valuation and Present Value in Microeconomics

Question 1

Two firms have identical expected future cash flows. Firm A's returns are highly correlated with the overall stock market; Firm B's returns are driven almost entirely by company-specific events uncorrelated with the market. Which firm should have a higher market valuation, and why?

• A. Firm A, because market-correlated returns are more predictable and therefore safer
• B. Firm B, because its idiosyncratic risk means it pays higher dividends to attract investors
• C. Firm B, because its risk is idiosyncratic and can be diversified away, so investors require no risk premium for it — a lower discount rate implies higher value
• D. Both firms have identical valuations since their expected cash flows are the same

Answer: (C)

This question tests the key insight about diversifiable versus non-diversifiable risk. Firm B's risk is idiosyncratic — investors who hold a diversified portfolio bear none of it, because bad outcomes at Firm B are offset by other holdings. Rational investors therefore require no risk premium for idiosyncratic risk, resulting in a lower discount rate and higher valuation. Firm A's risk is systematic (correlated with the market) and cannot be diversified away, so investors demand a risk premium — a higher discount rate and thus lower valuation — despite identical expected cash flows.

Question 2

A project requires a $1,000 upfront investment and is expected to return $1,050 in one year. The appropriate discount rate for comparable-risk investments is 8%. Should the firm invest?

• A. Yes, because the project earns a positive return of 5%
• B. No, because the NPV is negative — the present value of $1,050 at 8% is about $972, less than the $1,000 cost
• C. Yes, because any positive cash flow exceeds the cost of the project
• D. No, because returning more than invested in one year implies excessive risk

Answer: (B)

NPV = PV(cash flows) − cost = $1,050/1.08 − $1,000 ≈ $972 − $1,000 = −$28. A negative NPV means this project earns less than the 8% available on comparable-risk alternatives — it destroys value relative to the next-best use of the $1,000. The 5% return sounds positive in isolation, but the correct benchmark is the opportunity cost of capital (8%), not zero. The NPV rule embeds this comparison automatically: NPV > 0 means the project beats the market; NPV < 0 means it does not.

Question 3

Diversification reduces both the expected return and the variance of a portfolio.

• T. True
• F. False

Answer: False

Diversification reduces portfolio variance without reducing expected return — this is what makes it a 'free lunch' in finance. Expected portfolio return is simply the weighted average of individual asset expected returns, and combining assets doesn't change this. But when assets are imperfectly correlated, their risks partially cancel: bad outcomes on some assets coincide with good outcomes on others. Portfolio variance falls below the weighted average of individual variances. The insight is that risk reduction through diversification costs nothing in expected return, which is why any rational investor holds a diversified portfolio.

Question 4

An asset that generates higher expected returns than a risk-free government bond must be offering investors compensation for bearing systematic risk that cannot be diversified away.

• T. True
• F. False

Answer: True

In equilibrium, the extra expected return above the risk-free rate — the risk premium — compensates investors for bearing risk they cannot eliminate. Idiosyncratic risk can be diversified away by combining it with other uncorrelated assets, so rational investors who hold diversified portfolios bear none of it and will not pay a premium for bearing it. Only systematic risk (correlated with the broad market) survives diversification and therefore commands a risk premium. This is the core implication of the Capital Asset Pricing Model and of modern portfolio theory.

Question 5

Why does diversification reduce portfolio risk without reducing expected portfolio return? What is the mathematical and intuitive reason?

Model answer: Expected portfolio return is the weighted average of individual expected returns — combining assets doesn't change this. Portfolio variance, however, depends not just on individual variances but on covariances between assets. When assets are imperfectly correlated (covariance < product of standard deviations), the variance of their combination is less than the weighted average of their individual variances. Intuitively: when one asset has a bad year, another may have a good year, and these offsetting movements reduce the portfolio's overall swings without affecting the average outcome.

The formula var(aX + bY) = a²var(X) + b²var(Y) + 2ab·cov(X,Y) shows that if cov(X,Y) is negative or even less than var(X)·var(Y), the portfolio variance is below the weighted average variance. Perfect correlation (cov = σₓσᵧ) would mean no benefit from diversification; negative correlation provides the maximum benefit. This is why mixing a domestic stock fund with an international or bond fund reduces volatility — not because expected returns change, but because correlations are less than 1.