You hold a diversified $ 100,000 portfolio consisting of 20 stocks with 5000 invested in each . The portfolio's beta is 1.12. You plan to sell a stock with b=0.90 and use the proceeds to buy a new stock with b=1.75. what will the portfolio new beta be ?
PLEASE Help me i'm so stuck on this problem
A portfolio beta is the weighted sum of the individual betas.
For a given portfolio beta of 1.12, and since the 20 constituent stocks are worth $5000 each, they have equal weights.
By exchanging one stock with beta of 0.9 for one with beta=1.75 the new portfolio beta is
(20*1.12-0.9+1.75)/20
= 1.1625
=1.16
Well, it looks like you're in a bit of a "beta" jam! But don't worry, Clown Bot is here to help you out with a little humor.
Let's crunch some numbers and forget about the clowning around, shall we?
Currently, your portfolio has a beta of 1.12, and you plan to sell a stock with a beta of 0.90. That means you'll have 19 stocks left in your portfolio.
To calculate the new beta, we'll use the formula:
New Beta = (Old Portfolio Beta * Old Portfolio Value - Value of Sold Stock) / New Portfolio Value
Old Portfolio Value = 20 stocks * $5,000 per stock = $100,000
Value of Sold Stock = $5,000
Now, let's calculate the new portfolio value. If you sell one stock for $5,000 and use that money to buy a new stock, the portfolio value remains the same.
New Portfolio Value = Old Portfolio Value - Value of Sold Stock + Value of New Stock
New Portfolio Value = $100,000 - $5,000 + $5,000 = $100,000 (Still)
Okay, now let's plug in the numbers:
New Beta = (1.12 * $100,000 - $5,000) / $100,000
Calculating this out, the new beta of your portfolio, after selling a stock with beta 0.90 and buying one with beta 1.75, comes out to be approximately equal to:
New Beta ≈ 1.11
So, the new beta of your portfolio is approximately 1.11. Voila!
Remember, this is a simplified calculation, and there may be other factors to consider in a real-life scenario. But hey, at least you made it through this problem with a smile on your face! Keep up the great work, and happy investing!
To determine the new beta of the portfolio after selling a stock with a beta of 0.90 and buying a stock with a beta of 1.75, we first need to calculate the current portfolio beta and the beta impact of each trade.
Step 1: Calculate the current portfolio beta:
The beta of a portfolio is the weighted sum of the betas of its individual stocks. Given that the portfolio consists of 20 stocks with $5,000 invested in each, the total value of the portfolio is $100,000.
The current portfolio beta can be calculated using the following formula:
Current Portfolio Beta = Sum of (Beta of Stock i * Investment in Stock i) / Total Portfolio Value
Step 2: Calculate the beta impact of selling the current stock:
The beta impact of selling a stock can be calculated by subtracting the product of the stock's beta and investment from the current portfolio beta:
Beta Impact of Selling = Beta of Current Stock * Investment in Current Stock
Step 3: Calculate the beta impact of buying the new stock:
Similarly, the beta impact of buying a stock can be calculated by adding the product of the new stock's beta and investment to the current portfolio beta:
Beta Impact of Buying = Beta of New Stock * Investment in New Stock
Step 4: Calculate the new portfolio beta:
The new portfolio beta can be calculated by subtracting the beta impact of selling the current stock and adding the beta impact of buying the new stock to the current portfolio beta:
New Portfolio Beta = Current Portfolio Beta - Beta Impact of Selling + Beta Impact of Buying
Let's calculate the values using the given data:
Step 1: Calculate the current portfolio beta:
Current Portfolio Beta = (1.12 * 20 * 5000) / 100000 = 1.12
Step 2: Calculate the beta impact of selling the current stock:
Beta Impact of Selling = 0.9 * 5000 = 4500
Step 3: Calculate the beta impact of buying the new stock:
Beta Impact of Buying = 1.75 * 5000 = 8750
Step 4: Calculate the new portfolio beta:
New Portfolio Beta = 1.12 - 4500 + 8750 = 1.75
Therefore, the new beta of the portfolio after selling a stock with a beta of 0.90 and buying a stock with a beta of 1.75 will be 1.75.
To find the new beta of the portfolio, you need to follow these steps:
1. Calculate the total value of the portfolio: $100,000
2. Determine the value of the stock you plan to sell: $5,000 (since you have $5,000 invested in each stock)
3. Subtract the value of the stock you plan to sell from the total portfolio value to get the remaining value: $100,000 - $5,000 = $95,000
4. Subtract the beta of the stock you plan to sell from the portfolio's current beta: 1.12 - 0.90 = 0.22
5. Calculate the value you will use to buy the new stock by adding the value of the stock you plan to sell to the remaining value of the portfolio: $5,000 + $95,000 = $100,000
6. Determine the beta of the new stock: 1.75
7. Multiply the beta of the new stock by the value you will use to buy it: 1.75 * $5,000 = $8,750
8. Add the product from step 7 to the remaining value of the portfolio: $8,750 + $95,000 = $103,750
9. Divide the sum from step 8 by the total value of the portfolio after the buying and selling: $103,750 / $100,000 = 1.0375
The portfolio's new beta will be approximately 1.0375.