Explanation
Since the investor is investing 115% of their savings in the portfolio, this means they are borrowing 15% of funds at the risk-free rate and investing the entire amount (115%) in the market portfolio.
Calculation:
- Investment in portfolio: 115%
- Borrowing (negative investment in risk-free asset): -15%
- Risk-free rate: 8%
- Portfolio expected return: 17%
Expected return formula:
E[r]=(wrf×rrf)+(wp×rp)
E[r]=(−15%×8%)+(115%×17%)
E[r]=(−0.15×0.08)+(1.15×0.17)
E[r]=(−0.012)+(0.1955)
E[r]=0.1835=18.35%
Key Points:
- The investor is using leverage by borrowing at the risk-free rate
- The beta (1.2) and standard deviation (5.5%) are not needed for this calculation
- The expected return increases due to the leverage effect
- This demonstrates the concept of the Capital Market Line (CML) where investors can achieve higher returns by borrowing at the risk-free rate to invest more in the market portfolio