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:
We are given:
- Total transaction costs for selling = $45.00
- Brokerage commission = $25.00
- Number of shares = 1,100
Now let's calculate:
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:
We are given:
- Total transaction costs for buying = $40.20
- Brokerage commission = $25.00
- Number of shares = 1,100
Now let's calculate:
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:
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:
- What are the advantages of using limit orders over market orders in reducing transaction costs?
- How does the bid/ask spread change during high volatility in stocks?
- What factors determine the bid/ask spread in different markets like NYSE and NASDAQ?
- How does the size of your trade affect the bid/ask spread?
- 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
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