NO.PZ2023103101000059
问题如下：
Q. A hedge fund with net capital of GBP500 million has borrowed an additional GBP200 million at 4.5% per annum. The current-year return of the fund is 15%. What would have been the return if the fund had not added any leverage?选项：
A.10.70% B.12.00% C.19.20%解释：
B is correct.
Using Equation 2,
rL = Leveraged portfolio return/Cash position = [r × (Vb+Vc) – (Vb × rb)]/Vc.Or, after re-arranging the formula,r= ( Vc×rL )+(Vb×rb)(Vc+Vb).Substituting rL = 0.15, Vb = 200, Vc = 500, rb = 0.045,r = (500 × 0.15) + (200 × 0.045)/(200 + 500) = 12%.Since leverage magnifies return when the borrowing cost is lower than asset returns, the unleveraged asset return must be lower than 15%.
难道不应该这么算吗？？：
基金的净资本为5亿英镑，借入的资金为2亿英镑，所以总资本为7亿英镑。
如果基金今年的回报率为15%，那么总收益为：
7亿英镑 × 15% = 1.05亿英镑。
接下来，我们需要从总收益中扣除借款的利息费用。借入的2亿英镑的年利率为4.5%，所以一年的利息为：
2亿英镑 × 4.5% = 900万英镑。
扣除利息费用后的净收益为：
1.05亿英镑 - 900万英镑 = 9600万英镑。
如果没有使用杠杆，基金的资本仍为原始的5亿英镑。没有借款，也就无需支付利息，所以净收益仍然为9600万英镑。此时的回报率为：
9600万英镑 ÷ 5亿英镑 = 19.2%。
因此，如果对冲基金没有使用任何杠杆，其回报率将是19.2%。
