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Yvonne0719 · 2024年10月05日

麻烦老师讲解一下题目思路和用的公式，谢谢

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NO.PZ2023122201000070

问题如下：

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：

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%.

（500+200）*rA=200*4.5%+500*15%，反解出rA=12%

麻烦老师讲解一下题目思路和用的公式，谢谢

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pzqa35 · 2024年10月08日

嗨，爱思考的PZer你好：


这道题目是考察我们对于leveraged return的一个计算哈，老师在课堂中给我们讲到了一个比较好记的公式就是rA*VA=rD*VD+rE*VE, 也就是资产的收益就等于负债的收益加上所有者权益的收益。

根据题目，VD=200，rD=4.5%, rE=15%, VE=500，VA=200+500=700，带入公式：

700*rA=200*4.5%+500*15%，反解出rA=12%

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NO.PZ2023122201000070 问题如下 A hee funwith net capitof GBP500 million hborroweaitionGBP200 million 4.5% per annum. The current-yereturn of the funis 15%. Whwoulhave been the return if the funhnot aeany leverage? A.10.70% B.12.00% C.19.20% rL= Leverageportfolio return/Cash position = [r × (Vb +V– (Vb × rb)]/Vc.Or, after re-arranging the formula,r= [(Vc × rL ) + (Vb × rb)]/(Vc + V.Substituting rL= 0.15, V200, V500, r0.045,r = (500 × 0.15) + (200 × 0.045)/(200 + 500) = 12%.Sinleverage magnifies return when the borrowing cost is lower thasset returns, the unleverageasset return must lower th15%.（500+200）*rA=200*4.5%+500*15%，反解出rA=12% current-yereturn of the funis 15%. 15% 为什么不是整个asset的收益呢？

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