Final answer:
After tilting a portfolio with a 20% expected return towards a security with a 5% return by 1%, the expected return of the portfolio would slightly decrease to approximately 19.95%. However, due to the small size of the tilt and the high expected return of the rest of the portfolio, it remains nominally around 20%.
Step-by-step explanation:
If a portfolio with an expected return of 20% is tilted toward a security with an expected return of 5%, and the tilt size is 1%, then the majority of the portfolio is still expected to earn the higher rate of return. The portfolio's new expected return can be approximated by reducing the original expected rate of return proportionally based on the size of the tilt toward the lower-yielding security. As the tilt size is 1%, this means that 99% of the portfolio is still expected to earn a 20% return, while 1% of the portfolio is expected to earn a 5% return. Thus, the expected return of the portfolio after the tilt would be slightly less than the original 20%.
Considering the given risk-free rate of 50 basis points (0.50%), and ignoring the compounding impact over multiple periods, the adjustment due to the tilt towards the lower returning security would have a minor effect. This is because the tilt size is small relative to the total portfolio.
To calculate the adjusted expected return after the tilt, we can use the formula:
Adjusted expected return = (Portfolio percentage at higher return × Higher return) + (Portfolio percentage at lower return × Lower return)
Adjusted expected return = (99% × 20%) + (1% × 5%)
Adjusted expected return = 19.95% + 0.05%
Adjusted expected return = 20%
It turns out that the expected return remains nearly the same because the tilt size is minimal. This demonstrates how a small tilt towards a lower-earning asset affects the overall portfolio's expected rate of return. Full impact of the tilt would need to consider additional variables such as the volatility, correlations among assets, and the investment horizon.