ATTN Finance Gurus! MBA student in need of a little help with homework.

T

TheShooter

Okay, I've been looking at these problems so long that my head is starting to spin. Can someone please give me an idea as to how I approach and solve these two problem?

Here we go...
First Problem:

Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7,500 and to use these proceeds to buy another stock for your portfolio. Assume the new stock's beta is equal to 1.75. Calculate your portfolio's new beta.


Second Problem:
The Kish Investment Fund, in which you plan to invest some money, has a total capital of $500 million invested in 5 stocks.

StockA- Investment 160 million, beta 0.5 StockB- Investment 120 million, beta 2.0 StockC- Investment 80 million, beta 4.0 StockD- Investment 80 million, beta 1.0 StockE- Investment 60 million, beta 3.0

The beta coefficient for a fund like Kish Investment can be found as a weighted average of the fund's investments. The current risk-free rate is 6%, whereas market returns have the following estimated probability distribution for the next period.

Probability 0.1 Market Return 7%, Probability 0.2 Market Return 9%, Probability 0.4 Market Return 11%, Probability 0.2 Market Return 13%, Probability 0.1 Market return 15%.

Suppose Bridget Nelson, the president, receives a proposal for a new stock. The investment needed to take a position in the stock is $50 million, it will have an expected return of 15%, and its estimated beta coefficient is 2.0. Should the new stock be purchased? At what expected rate of return should the fund be indifferent to purchasing the stock?


Thanks!:confused:
 
Here we go...
First Problem:

Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7,500 and to use these proceeds to buy another stock for your portfolio. Assume the new stock's beta is equal to 1.75. Calculate your portfolio's new beta.

------------------------------

20 Stocks = $150k invested at a Beta of 1.12

You sell 1/20'th of your account that had a Beta of 1.00. Since this is less than the average 1.12 beta, the new beta for the remaining 19 stocks should be higher than the original beta.

[ 20 x (1.12) - (1.00) ] / 19 = 1.1263 [new beta]

[ 19 x (1.1263) + 1.75 ] * 20 = 1.157 [new beta with new stock added]

So the new BETA would be 1.157 with the new stock added to it.
 
Second Problem:
The Kish Investment Fund, in which you plan to invest some money, has a total capital of $500 million invested in 5 stocks.

StockA- Investment 160 million, beta 0.5 StockB- Investment 120 million, beta 2.0 StockC- Investment 80 million, beta 4.0 StockD- Investment 80 million, beta 1.0 StockE- Investment 60 million, beta 3.0

The beta coefficient for a fund like Kish Investment can be found as a weighted average of the fund's investments. The current risk-free rate is 6%, whereas market returns have the following estimated probability distribution for the next period.

Probability 0.1 Market Return 7%, Probability 0.2 Market Return 9%, Probability 0.4 Market Return 11%, Probability 0.2 Market Return 13%, Probability 0.1 Market return 15%.

Suppose Bridget Nelson, the president, receives a proposal for a new stock. The investment needed to take a position in the stock is $50 million, it will have an expected return of 15%, and its estimated beta coefficient is 2.0. Should the new stock be purchased? At what expected rate of return should the fund be indifferent to purchasing the stock?
More...
-------------------------

Stock A has a weight of (160/500) x Beta .5
Stock B has a weight of (120/500) x Beta 2.0
Stock C has a weight of (80/500) x Beta 4.0
Stock D has a weight of (80/500) x Beta 1.0
Stock E has a weight of (60/500) x Beta 3.0

Total BETA for all stocks is 1.8

I will solve the rest later ... I have to run

aphie
 
sum=sum of the betas
n=number of individual stocks, provided equal ponderations
bm=original beta
bm2=new beta

s n / bm =
so s 22.4 =
s 1 - 1.75 + n / bm2 =
so
23.15 20 / 1.1575 =

so your new beta would be 1.1575
About the same beta as Aphie :).



OHLC
 
fyi - while beta shows a stock's risk relative to the market (investment in isolation), it doesn't show how that investment would make the portfolio better or worse - you need to use correlation coefficients for that.
 
sum(1-5 x = ) ax at / bx * portfolio's beta =
with x an integer ranging from 1 to 5
a being the allocation for a stock
at being the total asset allocated
b being the beat of a stock

as a consequence this portfolio has a beta of 1.8

With a return of 15%, the stock is not to be purchased (19.8% for the portfolio).

>At what expected rate of return should the fund be indifferent >to purchasing the stock?

Not sure about "indifferent"

19.8% if indifferent means same expected return for the stock than the fund and 'expected return' applies to the stock.

If 'expected return' applies to the market, the fund should be indifferent to the purchase at 8.33%


OHLC







 
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