Math Problem Statement

Transaction costs  In late December you decide to sell a losing position that you hold in Twitter so you can capture the loss and use it to offset some capital​ gains, thus reducing your taxes for the current year.​ However, since you believe that Twitter is a good​ long-term investment, you wish to buy back your position in February next year. You call your Charles Schwab brokerage account manager and request that he sell your

1 comma 1001,100

shares of Twitter and buy them back in February. Charles Schwab charges a commission of

​$2525

for​ broker-assisted trades.

a. Suppose that your total transaction costs for selling the

1 comma 1001,100

shares of Twitter in December were

​$45.0045.00.

What was the​ bid/ask spread for Twitter at the time your trade was​ executed?

b. Given that Twitter is listed on the​ NYSE, do your total transaction costs for December seem​ reasonable? Explain why or why not.

c. When your February statement arrives in the​ mail, you see that your total transaction costs for buying the

1 comma 1001,100

shares of Twitter were

​$40.2040.20.

What was the​ bid/ask spread for Twitter at the time your trade was​ executed?

d. What are your total​ round-trip transaction costs for both selling and buying the​ shares, and what could you have done differently to reduce the total​ costs?

Question content area bottom

Part 1

a. The​ bid/ask spread for​ Twitter, at the time your trade was​ executed, is

​$enter your response here.

​ (Round to four decimal​ places.)

Part 2

b. Given that Twitter is listed on the​ NYSE, do your total transaction costs for December seem​ reasonable? Explain why or why not.

​"Twitter is listed on the​ NYSE, a broker market.​ So, had Charles Schwab routed the order to the​ NYSE, it could have been executed against a buy​ order, and total transaction costs would have been only the

​$2525

brokerage commission. But transaction costs included half the​ bid/ask spread per share​ traded, so​ either: (i) the order went to the​ NYSE, no public buy order was​ available, and the market maker bought the

1 comma 1001,100

shares for her inventory​ (at a cost of half the​ bid/ask spread per​ share) or​ (ii) Charles Schwab routed the order to a dealer market like​ NASDAQ, and a market maker added the shares to her inventory​ (at half the spread per​ share)."

This statement is

▼   true

false

.

​ (Select the best answer from the​ drop-down menu.)

Part 3

c. The​ bid/ask spread for​ Twitter, at the time your trade was​ executed, is

​$enter your response here.

​(Round to four decimal​ places.)

Part 4

d. Your total​ round-trip transaction costs for both selling and buying the shares is

​$enter your response here.

​(Round to the nearest​ cent.)

Part 5

What could you have done differently to reduce the total​ costs?  ​(Select the best answer​ below.)

A.

Costs could have been reduced by placing both trades online with a request for routing to the NYSE where the chance of crossing with other public orders is greatest.

B.

Costs could have been reduced by placing both trades with a market maker.

The bid/ask spread for Twitter, at the time your trade was executed, is $(Round to four decimal places.)This statement is(Select the best answer from the drop-down menu.)The bid/ask spread for Twitter, at the time your trade was executed, is $(Round to four decimal places.)Your total round-trip transaction costs for both selling and buying the shares is $(Round to the nearest cent.))

Solution

Part 1: a. Bid/Ask Spread for Selling the Shares

To calculate the bid/ask spread for Twitter when selling the 1,100 shares in December, we can use the following formula:

Bid/Ask Spread per share=Total Transaction CostBrokerage CommissionNumber of Shares\text{Bid/Ask Spread per share} = \frac{\text{Total Transaction Cost} - \text{Brokerage Commission}}{\text{Number of Shares}}

We are given:

  • Total transaction costs for selling = $45.00
  • Brokerage commission = $25.00
  • Number of shares = 1,100

Now let's calculate:

Bid/Ask Spread per share=45.0025.001,100=20.001,100=0.0182\text{Bid/Ask Spread per share} = \frac{45.00 - 25.00}{1,100} = \frac{20.00}{1,100} = 0.0182

Thus, the bid/ask spread is $0.0182 per share.

Part 2: b. Are the Total Transaction Costs Reasonable?

Yes, the total transaction costs for December seem reasonable. Twitter is listed on the NYSE, a broker market, and the spread costs are reasonable considering that the market maker would have purchased the shares for their inventory. Either there was no public buy order available on the NYSE, or the order was routed to a dealer market like NASDAQ. The market maker would then add the shares to their inventory at half the spread per share, which is reflected in the transaction cost.

Part 3: c. Bid/Ask Spread for Buying the Shares

The formula is the same as for selling the shares:

Bid/Ask Spread per share=Total Transaction CostBrokerage CommissionNumber of Shares\text{Bid/Ask Spread per share} = \frac{\text{Total Transaction Cost} - \text{Brokerage Commission}}{\text{Number of Shares}}

We are given:

  • Total transaction costs for buying = $40.20
  • Brokerage commission = $25.00
  • Number of shares = 1,100

Now let's calculate:

Bid/Ask Spread per share=40.2025.001,100=15.201,100=0.0138\text{Bid/Ask Spread per share} = \frac{40.20 - 25.00}{1,100} = \frac{15.20}{1,100} = 0.0138

Thus, the bid/ask spread is $0.0138 per share.

Part 4: d. Total Round-Trip Transaction Costs

To find the total round-trip transaction costs, simply add the costs of selling and buying the shares:

Total Round-Trip Transaction Costs=45.00+40.20=85.20\text{Total Round-Trip Transaction Costs} = 45.00 + 40.20 = 85.20

So, the total round-trip transaction costs are $85.20.

Part 5: How Could You Reduce Total Costs?

The best option would be:

A. Costs could have been reduced by placing both trades online with a request for routing to the NYSE where the chance of crossing with other public orders is greatest.

This would avoid relying on a market maker and reduce the bid/ask spread costs.


Do you need further details or clarification? Here are some additional related questions you might find interesting:

  1. What are the advantages of using limit orders over market orders in reducing transaction costs?
  2. How does the bid/ask spread change during high volatility in stocks?
  3. What factors determine the bid/ask spread in different markets like NYSE and NASDAQ?
  4. How does the size of your trade affect the bid/ask spread?
  5. How do online brokerage platforms compare to traditional broker-assisted trades in terms of cost?

Tip: Always consider placing trades during high-volume market hours to minimize bid/ask spreads.

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Math Problem Analysis

Mathematical Concepts

Financial Mathematics
Transaction Costs
Bid/Ask Spread

Formulas

Bid/Ask Spread = (Total Transaction Cost - Brokerage Commission) / Number of Shares

Theorems

-

Suitable Grade Level

University Level - Finance or Economics