Lecture 2: Arbitrage & Financial Decision Making

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Last updated 8:36 PM on 4/16/26
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19 Terms

1
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How do you analyze costs & benefits?

  • Find NPV (net present value) to see if an opportunity is profitable

Suppose a jeweler can trade 400 ounces of silver for 10 ounces of gold today

  • preferences don’t matter in competitive market where you can make a profit!

<ul><li><p>Find NPV (net present value) to see if an opportunity is profitable</p></li></ul><p>Suppose a jeweler can trade 400 ounces of silver for 10 ounces of gold today</p><ul><li><p>preferences don’t matter in competitive market where you can make a profit!</p></li></ul><p></p>
2
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What happens when competitive market prices are not available?

If unsure can buy/sell at same price → prices may be one sided

  • preferences matter!

<p>If unsure can buy/sell at same price → prices may be one sided</p><ul><li><p>preferences matter!</p></li></ul><p></p>
3
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What is the time value of money?

The difference in value between money today & money in the future due to time value of money

<p>The difference in value between money today &amp; money in the future due to time value of money</p><p></p>
4
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How do you compare costs at different points in time?

Must adjust by discounting in order to compare between time

<p>Must adjust by discounting in order to compare between time</p>
5
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*How do you covert between dollars today, gold, euros, or dollars in the future?

Dollars today / gold price = ounces of gold today

Ounces of gold today x gold price = dollars today

Dollars today x exchange rate = euros today

Euros today / exchange rate = dollars today

Dollars today x (1+rf) = dollars in 1 year

Dollars in 1 year / (1+rf) = dollars today

<p>Dollars today / gold price = ounces of gold today</p><p>Ounces of gold today x gold price = dollars today</p><p>Dollars today x exchange rate = euros today</p><p>Euros today / exchange rate = dollars today</p><p>Dollars today x (1+rf) = dollars in 1 year</p><p>Dollars in 1 year / (1+rf) = dollars today</p>
6
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What is NPV & NPV decision rule?

NPV = PV(benefits) - PV(costs)

NPV = PV(All project cash flows)

  • Choose the alternative with the highest NPV

  • Accept projects with + NPV

  • Reject projects with - NPV

* The NPV of buying & selling securities in a competitive market is 0!

<p>NPV = PV(benefits) - PV(costs)</p><p>NPV = PV(All project cash flows)</p><ul><li><p>Choose the alternative with the highest NPV</p></li><li><p>Accept projects with + NPV</p></li><li><p>Reject projects with - NPV</p></li></ul><p><strong>* The NPV of buying &amp; selling securities in a competitive market is 0!</strong></p><p></p>
7
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When should you max NPV and when should you not?

In a competitive market → should always maximize NPV regardless of preferences

If not in a competitive market → don’t always max NPV preferences matter! Because can’t buy/sell at the same price

8
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What is arbitrage, arbitrage opportunity, & normal market?

Arbitrage - buying & selling equivalent goods in different markets to take advantage of price difference (buy low, sell high)

Arbitrage opportunity - when possible to make profit without taking risk or making investment

Normal market - competitive market with NO arbitrage opportunities

  • arbitrage doesn’t exist in normal/compettiive market bc goods sold/bought for same price!

<p>Arbitrage - buying &amp; selling equivalent goods in different markets to take advantage of price difference (buy low, sell high)</p><p>Arbitrage opportunity - when possible to make profit without taking risk or making investment</p><p>Normal market - competitive market with NO arbitrage opportunities </p><ul><li><p>arbitrage doesn’t exist in normal/compettiive market bc goods sold/bought for same price!</p></li></ul><p></p>
9
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What is law of one price?

If there are equivalent investment opportunities trading at the same time in different competitive markets, they must trade for same price in both markets!

  • in efficient markets, arbitrage opportunites adjust according to supply & demand

* find the cost of bond with no arbitrage!

<p>If there are equivalent investment opportunities trading at the same time in different competitive markets, they must trade for <strong>same price </strong>in both markets!</p><ul><li><p>in efficient markets, arbitrage opportunites adjust according to supply &amp; demand</p></li></ul><p><strong>* find the cost of bond with no arbitrage!</strong></p><p></p>
10
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What is an undervalued arbitrage opportunity?

If the bond is priced less than the actual value, there is an arbitrage opportunity to buy low!

  • compare with cost of bond with no arbitrage in order to tell if under or over valued!

<p>If the bond is priced less than the actual value, there is an arbitrage opportunity to buy low!</p><ul><li><p>compare with cost of bond with no arbitrage in order to tell if under or over valued!</p></li></ul><p></p>
11
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What is an overvalued arbitrage opportunity?

When the bond price is priced higher than actual value, there is an arbitrage opportunity to sell high!

  • short sell (borrow bond & sell) → used when want to sell but don’t own bond

  • compare with cost of bond with no arbitrage in order to tell if under or over valued!

<p>When the bond price is priced higher than actual value, there is an arbitrage opportunity to sell high!</p><ul><li><p>short sell (borrow bond &amp; sell) → used when want to sell but don’t own bond</p></li><li><p>compare with cost of bond with no arbitrage in order to tell if under or over valued!</p></li></ul><p></p>
12
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How do you find the interest rate from bond prices?

If know the price of a risk-free bond, can use

Price(security) = PV(all cash flows paid by security)

  • solve for interest rate by using formula, including bond & security prices

<p>If know the price of a risk-free bond, can use</p><p>Price(security) = PV(all cash flows paid by security)</p><ul><li><p>solve for interest rate by using formula, including bond &amp; security prices</p></li></ul><p></p>
13
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What is the result for any financing activity in a normal market?

The results are the same & their NPV’s are the same!

<p>The results are the same &amp; their NPV’s are the same!</p>
14
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What is value additivity?

  • To max the value of entire firm, managers should make decisions that maximize NPV

Price(C) = Price(A + B) = Price(A) + Price(B)

<ul><li><p>To max the value of entire firm, managers should make decisions that maximize NPV</p></li></ul><p>Price(C) = Price(A + B) = Price(A) + Price(B)</p>
15
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What is the price of risk?

Risk - when the actual outcome may differ from expected outcome

  • when investment payments depend on strong or weak economic conditions

→ the market price of risk-free bond is higher than risky bond as we are willing to pay more for no risk

<p>Risk - when the actual outcome may differ from expected outcome</p><ul><li><p>when investment payments depend on strong or weak economic conditions</p></li></ul><p>→ the market price of risk-free bond is higher than risky bond as we are willing to pay more for no risk</p><p></p>
16
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What is risk aversion & risk premium?

Risk aversion - personal cost of losing a dollar in bad times is greater than benefit of extra dollar in good times

<p>Risk aversion - personal cost of losing a dollar in bad times is greater than benefit of extra dollar in good times</p>
17
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How do you find the price, expected return, & risk premium of risky security A?

Risk premium is a percentage = expected return - risk free interest rate

<p>Risk premium is a percentage = expected return - risk free interest rate</p>
18
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How do you convert dollars today & dollars in one year with risk?

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19
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What is arbitrage with transaction costs?

Commissions paid to broker

  • Bid-ask spread: difference of price you receive when you sell (bid price) and when you buy (ask price) a security

  • small cost for most financial markets

<p>Commissions paid to broker</p><ul><li><p>Bid-ask spread: difference of price you receive when you sell (bid price) and when you buy (ask price) a security</p></li><li><p>small cost for most financial markets</p></li></ul><p></p>