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Mice21 [21]
4 years ago
10

3. You have $100 to invest. The price of XYZ stock is $100. You sell short one share of XYZ and then invest all available funds

(your initial $100 and any short-sale proceeds) in one-year zero-coupon bonds with 5% yield to maturity. One year later, the price of XYZ is $90. There are no dividends. What is the HPR on your initial $100?
Business
1 answer:
tigry1 [53]4 years ago
5 0

Answer:

HPR = holding period Return is 20%

Explanation:

  • Given original Investment = $100
  • Short sale proceeds for 1 share = $100
  • Investment made of $100 + short sale proceeds of $100 at 5% YTM.
  • So Maturity Value = Investment x (1+YTM)^number of years  
  • = 200 x (1 + 0.05)^1 = 210  

 

  • Therefore, In order to cover Short sale of 1 share, we will have to buy 1 share at a closing value of $90  
  • As such, holding period Return = (Investment proceeds from ZCB - Buying price of stock - Investment amount) / Investment Amount  
  • = (210 - 90 - 100) / 100 = 0.2 or 20%  

 

  • Hence, HPR = holding period Return is 20%  
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Using the continuous compounding equation, if someone invested $5,000 at an interest rate of 3.5%, and someone else invested $5,
UNO [17]

Answer:

Therefore after 16.26 unit of time, both accounts have same balance.

The both account have $8,834.43.

Explanation:

Formula for continuous compounding :

P(t)=P_0e^{rt}

P(t)=  value after t time

P_0= Initial principal

r= rate of interest annually

t=length of time.

Given that, someone invested $5,000 at an interest 3.5% and another one  invested $5,250 at an interest 3.2% .

Let after t year the both accounts have same balance.

For the first case,

P= $5,000, r=3.5%=0.035

P(t)=5000e^{0.035t}

For the second case,

P= $5,250, r=3.5%=0.032

P(t)=5250e^{0.032t}

According to the problem,

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\Rightarrow e^{0.003t}=\frac{21}{20}

Taking ln both sides

\Rightarrow lne^{0.003t}=ln(\frac{21}{20})

\Rightarrow 0.003t}=ln(\frac{21}{20})

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\Rightarrow t= 16.26

Therefore after 16.26 unit of time, both accounts have same balance.

The account balance on that time is

P(16.26)=5000e^{0.035\times 16.26}

              =$8,834.43

The both account have $8,834.43.

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3 years ago
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