Questions: Yang Bai is investing 10,000 and wants a portfolio that is 80% stocks and 20% bonds. She has decided to accomplish this using just 2 exchange-traded funds (ETFs): a stock ETF trading for 50 per share and a bond ETF trading for 100 for share. What should she do to meet her asset allocation goal?

Yang Bai is investing 10,000 and wants a portfolio that is 80% stocks and 20% bonds. She has decided to accomplish this using just 2 exchange-traded funds (ETFs): a stock ETF trading for 50 per share and a bond ETF trading for 100 for share. What should she do to meet her asset allocation goal?
Transcript text: Yang Bai is investing \$10,000 and wants a portfolio that is $80 \%$ stocks and $20 \%$ bonds. She has decided to accomplish this using just 2 exchange-traded funds (ETFs): a stock ETF trading for $\$ 50$ per share and a bond ETF trading for $\$ 100$ for share. What should she do to meet her asset allocation goal?
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Solution

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Solution Steps

To meet her asset allocation goal, Yang Bai needs to determine how many shares of each ETF to buy. She wants 80% of her investment in stocks and 20% in bonds. We can calculate the dollar amount for each type of investment and then determine the number of shares to buy based on the price per share of each ETF.

Step 1: Determine the Dollar Amounts for Each Investment

Yang Bai wants to invest a total of \$10,000 with an allocation of 80% in stocks and 20% in bonds. We calculate the dollar amounts for each type of investment as follows:

\[ \text{Stock Investment} = \$10,000 \times 0.80 = \$8,000 \]

\[ \text{Bond Investment} = \$10,000 \times 0.20 = \$2,000 \]

Step 2: Calculate the Number of Shares to Buy

Next, we determine the number of shares to buy for each ETF based on their prices. The stock ETF trades for \$50 per share, and the bond ETF trades for \$100 per share.

\[ \text{Number of Stock Shares} = \frac{\$8,000}{\$50} = 160 \text{ shares} \]

\[ \text{Number of Bond Shares} = \frac{\$2,000}{\$100} = 20 \text{ shares} \]

Final Answer

\[ \boxed{\text{Number of Stock Shares} = 160 \text{ shares}} \]

\[ \boxed{\text{Number of Bond Shares} = 20 \text{ shares}} \]

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