Topic 1: Arbitrage and Financial Decision Making

Question 1

What is the Valuation Principle?

Answer 1

• The benefits and costs of decisions should be evaluated using competitive market prices
• And when the value of the benefits exceeds the value of the costs, the investment decision should be made

Question 2

When the Net Value (NV) is positive….

Answer 2

The value of the benefits exceeds the value of the costs

Question 3

What is a competitive market?

Answer 3

A market in which goods can be bought and sold at the same price

Question 4

What is a risk free interest rate or discount rate rf?

Answer 4

The interest rate at which money can be borrowed or lent without risk.

Question 5

Interest Rate Factor =

Answer 5

1 + rf

• £1 + rf in the future and (vice versa)

Question 6

Discount Factor =

Answer 6

1/(1+rf)

• £1 in the future is worth 1/(1+rf) today and (vice versa)

Question 7

What is the Net Present Value (NPV)?

Answer 7

The NPV of an investment is the present value of its benefits minus the the present value of its costs

Question 8

NPV equation

Answer 8

NPV = PV (benefits) - PV (costs)

Question 9

What is the Net Present Value Decision Rule?

Answer 9

When making an investment decision, take the alternative with the highest Net Present Value

Question 10

Brief of Net Present Value Decision Rule?

Answer 10

• The NPV of not doing a project is zero
• When deciding whether to accept or reject a project, we should accept only if the NPV is positive
• Any positive NPV project will increase the value of the firm
• Use of market prices means this is true regardless of preferences or needs, and regardless of cash availability
• If choosing between different alternative investments/projects, choose the one with highest NPV.

Question 11

What is the Law of One Price?

Answer 11

If equivalent investment opportunities trade simultaneously in different competitive markets, then they must trade for the same price in both markets

Question 12

What is Arbitrage?

Answer 12

The practice of buying and selling equivalent goods in different markets to take advantage of a price difference.

Question 13

When does arbitrage opportunity occur?

Answer 13

When it is possible to make a profit without taking any risk or making any investment i.e. it its a strategy with a positive NPV

Question 14

What is a normal market?

Answer 14

A competitive market in which there are no arbitrage opportunities

Question 15

What are financial securities?

Answer 15

Investment opportunities that are traded in a financial market, typically using no-arbitrage arguments

Question 16

In a normal market, the following conditions must hold…

Answer 16

No Arbitrage price of a security

Price (security) = PV (All cash flows paid by the security)

• Same as saying that the NPV of either buying or selling a security is zero in a normal market
• If this is not true, then an arbitrage opportunity will exist by either buying or selling the security

Question 17

What is a bond?

Answer 17

A financial security that makes one or more guaranteed payments to the holder of known amounts at one or more known future date(s)

Question 18

What do simple arbitrage strategies assume?

Answer 18

Competitive market prices -> so all securities can be bought and sold at the same price

Question 19

In reality, what does trading in the financial market involve?

Answer 19

Transaction costs

Question 20

Give examples of transaction costs

Answer 20

• Commission fees to broker who buys and/or sells on your behalf
• Prices for buying (ask prices) are usually slightly higher than prices for selling (bid prices), which the true competitive price somewhere between

Question 21

What is an example of no-arbitrage prices where it can be used to infer the risk-free interest rate?

Answer 21

Government bonds

Question 22

View on government bonds

Answer 22

Typically viewed as being risk-free, so must provide the same cash flow as investing the equivalent amount at the risk-free rate i.e their return must be the risk-free rate

Question 23

How can firm value be created?

Answer 23

Through real investment projects to enter new markets or improving efficiency etc.

Question 24

Do trading securities in a normal market affect the firms value?

Answer 24

NO - they can only change the timing and/or risk of cash flows

Question 25

What is the separation principle?

Answer 25

The firm can separately consider whether it should undertake a project, and how it should be financed - Essentially when evaluating the NPV of possible projects, the way in which they are funded is irrelevant for whether they should be undertaken or not

Question 26

The Law of One Price also has implications for the prices of..

Answer 26

combinations, or portfolios, of securities

Question 27

If PV(C) = PV/(A+B) and A, B, C have the same risk then

Answer 27

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

Question 28

What is Risk Aversion?

Answer 28

Investors prefer to have a safe income rather than a risky one of the same average amount

Question 29

For the return on a risky asset...

Answer 29

we compute the expected return i.e. the return we expect to receive on average

Question 30

What is a Risk Premium?

Answer 30

The additional return that investors expect to earn to compensate them for a security's risk

Question 31

What to do when a cash flow is risky?

Answer 31

- We cannot compute its present value by using rf to discount the cash flow we expect on average - Instead we must use a rate rs that equals the risk-free interest rate plus an appropriate risk premium

Question 32

Equation for rs

Answer 32

rs = rf + (risk premium for investment s)

Question 33

If an investment has much more variable returns...

Answer 33

it must pay investors a higher risk premium

Question 34

Define Price of Risk Principle

Answer 34

The cost of losing a pound in bad times is greater than the benefit of an extra pound in good times

Question 35

The risk of a security must be evaluated in relation to the....

Answer 35

fluctuations of other investments in the economy

Question 36

The level of risk in terms of the cash flows alone does not....

Answer 36

determine the risk premium

Question 37

Link security risk premiums with the overall economy

Answer 37

A security's risk premium will be higher the more its returns tend to vary with the overall economy and the market index - e,g If the security's returns vary in the opposite direction of the market index, it offers insurance and will have a negative risk premium