Let’s consider an asset with a 20% standard deviation and a 10% expected arithmetic return. Applying the equation for Rg, this asset has an expected compounded return of 8% (10% – 20%2/2 = 8%)
What happens to the relationship between the arithmetic return and the compounded return when leverage is used?
Answer
Ignoring the cost of funding, if we increase the leverage, there is no additional improvement in return:
Incorporating the cost of funding leverage, the active return is reduced while the volatility remains proportional to the amount of leverage. The Sharpe ratio will decline even faster.
Using the same example, we could show that a portfolio with a leverage of 3× would have the same expected return as an unlevered portfolio if the cost of funding leverage were 2%: (3 × 10% – 2 × 2%) – (3 × 20%)2/2 = 8%
请问：最后加上cost of funding leverage的计算公式，是什么样的？为啥2%的cost是乘以2，麻烦帮讲解一下，谢谢。
