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Nesterboy [21]
3 years ago
9

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities,

X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills? Select one: $240; $360 $360; $240 $100; $240 $240; $160
Business
1 answer:
kozerog [31]3 years ago
5 0

Answer:

$240; $160

Explanation:

The computation is shown below:

As we know that

if there is 40% of money engaged in the risk portfolio is

= $1000 × 40%

= $400

Now amount in X is

= $400 × 0.60

= $240

And, the amount in Y is

= $400 × 0.40

= $160

hence, the last option is correct

All other valeus i.e. given in the question is not relevant. hence, ignored it

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To find the change in the price of the bonds, first need to find the price of individual Bond.

Bond Price is directly related to the change in the YTM of the bond. If the YTM rises by 2%, the price of the bond will fall.

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(WHEN YTM IS 8%)

Coupon Rate: 5%

Coupon Amount (PMT): $1,000 * 5% = $50/2 = $25 (Semi annual coupon amounts)

Number of years (NPER) = 13*2 = 26

YTM (rate) = 8%/2 = 4%

Face Value: $1000

Price (PV0) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

PV =pv(rate,nper,pmt,fv,type)

P0 =pv(4%,26,-25,-1000)

When input the formula in excel, we get PV as $760.26

(WHEN YTM RISES BY 2%, NEW YTM IS 10%)

Coupon Amount (PMT): $25 (Semi annual coupon amounts)

Number of years (NPER) = 26

YTM (rate) = 10%/2 = 5%

Face Value: $1000

Price (PV1) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

PV =pv(rate,nper,pmt,fv,type)

P1 =pv(5%,26,-25,-1000)

When input the formula in excel, we get PV as $640.62

CHANGE IN THE BOND PRICE OF BOND J DUE TO THE CHANGE IN THE YTM

%change = (P1 – P0)/P0

%change = ($640.62 - $760.26)/$760.26

%change = -18.68%

Therefore, with the increase in 2% YTM of BOND J, the price falls by 18.68%

Bond K :

(WHEN YTM IS 8%)

Coupon Rate: 11%

Coupon Amount (PMT): $1,000 * 11% = $110/2 = $55 (Semi annual coupon amounts)

Number of years (NPER) = 13*2 = 26

YTM (rate) = 8%/2 = 4%

Face Value: $1000

Price (PV0) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

PV =pv(rate,nper,pmt,fv,type)

P0 =pv(4%,26,-55,-1000)

When input the formula in excel, we get PV as $1,239.74

(WHEN YTM RISES BY 2%, NEW YTM IS 10%)

Coupon Amount (PMT): $55 (Semi annual coupon amounts)

Number of years (NPER) = 26

YTM (rate) = 10%/2 = 5%

Face Value: $1000

Price (PV1) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

PV =pv(rate,nper,pmt,fv,type)

P1 =pv(5%,26,-55,-1000)

When input the formula in excel, we get PV as $1,071.88

CHANGE IN THE BOND PRICE OF BOND K DUE TO THE CHANGE IN THE YTM

%change = (P1 – P0)/P0

%change = ($1071.88 - $1239.74)/$1239.74

%change = -13.54%

Therefore, with the increase in 2% YTM of BOND k, the price falls by 13.54%

SIMILALRY IF THE BOND PRICES FALLS BY 2%, the YTM WILL BE 6%/2 = 3% **(REFER THE IMAGE ATTACHED)

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Answer:

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Answer:

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