To calculate beta (β), use the formula:

β = ρ × (σᵢ / σₘ)
= 0.88 × (0.162 / 0.145)
= 0.88 × 1.117
= 0.983

So, the closest answer is 0.98.
Beta represents the sensitivity of the asset’s return to movements in the market return.

The capital allocation line (CAL) illustrates all possible combinations of a risk-free asset and a portfolio of risky assets. It shows the trade-off between expected return and total risk (standard deviation) for different allocations. The slope of the CAL is the Sharpe ratio of the risky portfolio. The security characteristic line shows the relationship between an individual asset’s excess returns and the market’s excess returns, not total risk.

The correlation between a risk-free asset and any risky asset is zero (0.0) since the risk-free asset has no variability in returns. This zero correlation allows for diversification benefits, which improve the portfolio’s overall risk-return profile compared to holding just one type of asset.

The beta of a risk-free asset is 0, and the beta of the market portfolio is 1.0. This investor uses leverage:

• They invest 1.5 times their own capital ($30,000 total / $20,000 of their own money = 1.5).

• Since all funds are in the market portfolio, and the risk-free portion is negative (borrowed), the portfolio beta = 1.5 × 1.0 = 1.5.

In simple terms: borrowing to invest more in the market increases your portfolio beta by the leverage amount.

We are asked to calculate beta using the standard formula:

β _{i} = \frac{Cov(R_{i},R_{m})}{σ^{2}_{m}}

In this case:

β _{i} = \frac{0.0108}{(0.20)^{2}} = \frac{0.0108}{0.04} = 0.27

If you’re given standard deviation of the market and using the covariance-based beta formula, you must square the standard deviation to get variance. It’s not that 0.20 is the variance — it’s the standard deviation, and you square it because the formula demands variance in the denominator.

According to capital market theory and CFA ethical guidelines, a suitable investment recommendation must align with the investor’s individual goals and risk tolerance. This means selecting the portfolio that lies on the highest indifference curve tangent to the capital allocation line. Simply maximizing return or Sharpe ratio does not consider investor preferences, making such recommendations unsuitable.

E(R _{GBK} ) = R _{f} + β _{GBK} × [E(R _{MKT} ) R _{f}]

To calculate expected return using the Capital Asset Pricing Model (CAPM), use the formula:

Expected Return = Risk-free rate + Beta × (Market return − Risk-free rate)

Now plug in the numbers:

= 0.04 + 0.75 × (0.10 − 0.04)
= 0.04 + 0.75 × 0.06
= 0.04 + 0.045
= 0.085 or 8.5%

So the correct answer is 8.5%.

Highly risk-averse investors have a strong preference for safety and stability. Rather than seeking high returns with greater risk, they prefer to preserve capital. As a result, they typically allocate most of their wealth to risk-free assets (e.g., government securities), avoiding the volatility associated with even optimal risky portfolios.