Chapter 27

Question 1

What is the time value of money?

Answer 1

• it’s all about how time works its magic on interest!
• Compounding: the accumulation of a sum of money where the interest earned on the sum earns additional interest -> you earn interest on the interest!
• example: suppose you put $1,000 in the bank today and leave it there for 30 years.
o if you earn interest of 8%, in 30 years, it will be worth $10,063
o if you earn interest of 10%, in 30 years, it will be worth $17,450

Question 2

What are two flavors of time value of money problems?

Answer 2

• depends on whether we are looking: o •forward into the future, or
•backwards into the past.
• if we are trying to find out the value of $ held today at some time in the future -> future value of a present sum.
• if we pretend to be in the future and are trying to find out the value today
of $ held in the future -+ present value of a future sum.
• see http://bit.ly/10a0uyE (it’s a Khan Academy video)

Question 3

Another look…

Answer 3

Another look.
• to compare sums from different times, we use the concept of
“present value” or “future value”
the present value of a future sum: the amount that would be needed today to produce that future sum at a certain interest rate.
• the future value of a sum: the amount that a sum of money NOW will be worth at some future date, when allowed to earn interest at a certain interest rate.

Question 4

What are the two formulas you need to remember

Answer 4

• and four variables for each formula:
• PV = the amount of money you have today
• FV = the amount of money in the future
• n= the number of periods in the future (usually measured
in years)
•r = the interest rate
Every ‘time value of money’ problem uses these variables.

Question 5

There are two formulas you need to remember

Answer 5

Future value - how much will a dollar held now be worth in year ‘n’?
general formula -> FV = PV * (1 + r)^n

example - if I put $1 in the bank today, and it earns interest of 10%:
• in one year, it would be worth [$PV x (1 + r )r] = 1 x (1.10)1 = $1.10
• in five years, it would be worth [$PV x (1 + r )n] = 1 x (1.10)5 = $1.61

There are two formulas you need to remember ..
Present value - how much is a dollar in year ‘n’ worth now?
FV
general formula -> PV = (1+7)n

example - if I want to have $1 in the bank in the future, and it will earn interest of 10% until then. How much will I need to deposit today?
• if I want the $1 one year from now, I must deposit today
FV/(1+r)n = 1/(1.10)1 = $0.9090 or 91¢
• if I want the $1 five years from now, I must deposit today
FV/(1+r)n = 1/(1.10)5 = $0.6209 or 62¢

Question 6

What happens if we change the interest rate(r)?

Answer 6

° as interest rates rise, the present value of the project becomes
smaller.
• it works the other way, too -> as rates drop, PV rises!
• THIS IS A KEY FEATURE OF TIME VALUE OF MONEY.
• I’ll show some examples in a minute.
Present value analysis helps explain why investment falls when the interest rate rises.

Question 7

What are the basic rules of thumb for PC analaysis

Answer 7

• greater weight is placed on earlier payments.
• the more ‘n’s there are (or the bigger the ‘n’), the higher PV will be.
• the higher the interest rate (‘r’), the lower PV will be.
o why? the higher PV means that later payments will be worth less, and so the sum of them will be lower. o riskier projects will have a higher ‘n’ which in turn means a lower PV -> they will be harder to justify. This makes sense.

Question 8

What’s compounding

Answer 8

• Compounding: the accumulation of a sum of money where the interest earned on the sum earns additional interest -> you earn interest on the interest!
• because of compounding, small differences in interest rates lead to big differences over time.

• Compounding: the accumulation of a sum of money where the interest earned on the sum earns additional interest.
• example: Buy $1,000 worth of Microsoft stock, hold for 30 years.
If rate of return = 8%, FV = $10,063
If rate of return = 10%, FV = $17,450

Question 9

The Rule of 7

Answer 9

• instead of the mathy formulas above, there’s a simple rule that
APPROXIMATES returns.
• the Rule of 70: If money grows at a rate of ‘x’ percent per year, that sum will double in about 70/x years.
• example:
• if interest rate is 5%, a deposit will double in about 14 years (70/5).
• if interest rate is 7%, a deposit will double in about 10 years (70/7).

Question 10

What’s risk aversion?

Answer 10

° a key concept in psychology and behavioral economics
•there are lots of definitions. My favorite is finance based:
a risk averse person prefers lower returns with known risks rather than higher returns with unknown risks.
The basic idea: human beings don’t like risk and uncertainty and so they will take steps to avoid or reduce it.

Question 11

What are the three types of people?

Answer 11

People are either
• risk averse - they avoid risk
•risk indifferent - they don’t care one way or the other
•risk seeking - they LIVE for risk

Question 12

Risk aversion in real life

Answer 12

• most people are risk averse -they dislike uncertainty.
* example; suppose you are offered the following gamble -> I toss a fair coin (that is, it’s not rigged in my favor -> there is a 50% probability of the coin landing ‘heads’ or ‘tails).
o if it lands heads, you win $1,000. o if it lands ‘tails, you lose $1,000.
• should you take this gamble?

Question 13

What is utility of wealth and diminishing marginal utility?

Answer 13

Utility of wealth is a subjective measure of vour happiness that depends on how rich vou are.
As wealth rises, the curve becomes flatter due to diminishing marginal utility: > the more wealth a person has, the less extra happiness he would get from an extra dollar of wealth.

Question 14

How do people manage the
general financial risk they face every day?
With insurance!

Answer 14

• how insurance works -> a person facing a risk pays a fee to another person (usually an insurance company), which in return:
o accepts part or all of that risk by o agreeing to compensate the insured person if a loss occurs.
• having insurance changes people’s behavior.

Question 15

Managing Risk with Insurance

Answer 15

• if you drive a car, you might get in an accident and cause damage to yourself or to others.
• you can accept all of the financial risk of an accident yourself. If you do this, you pay ALL the costs of an accident.
• insurance allows risks to be pooled -> the risk is “spread” among all the people the insurer insures.
• it’s better for 10,000 people to each bear 1/10,000 of the risk of someone’s house burning down than for one person to bear the entire risk alone.
• the people whose house DOESN’T burn down end up paying for the house that DOES burn down (through their premiums).
Everyone in the pool shares risks and costs.
• this “pooling of risks” can make a risk averse person better off.

Question 16

What’s adverse selection

Answer 16

• adverse selection: A high-risk person benefits more from insurance, so is more likely to purchase it.
o if you’re healthy, you may say, “I am not going to get sick. Why should I waste money on insurance?”
• but if you expect to become sick, you will say, “| am going to get sick, so l’d better get insurance so it will pay my expenses when I do.

• adverse selection: A high-risk person benefits more from insurance, so is more likely to purchase it.
o result: sick are more likely to buy insurance than healthy. o problem: what would happen to an insurance company, if all the people it insures have diabetes and require expensive medical care all the time? [Hint: not very good things]

Question 17

What’s Moral hazard

Answer 17

• Moral hazard: People with insurance have less incentive to avoid risky behavior.
o if you have insurance and know that an insurer will pay you if you crash your car, you may feel free to drive like a maniac. o if you have health insurance, you may feel free to eat 12 cheeseburgers a day.

Question 18

Remember both stocks and bonds are securities

Answer 18

• a security is a promise by its “seller” to make future payments to its buyer.
• the price of a security represents an estimate of its present financial “value.
• financial analysis to figure out what that “value” is.
• consider the difference:
• price - what it costs to buy a security.
o value - what you think it’s worth -> this is part science and part opinion.

Question 19

Both stocks and bonds are “securities”

Answer 19

• financial analysis tries to figure out what that “value” is.
• lots of uncertainty about what represents the proper value.
• part of that uncertainty relates to changes in prices over time.
° a security whose price changes a lot or very quickly is considered more “risky” than one whose price is stable.
• “risk” = the probability that you will not get the outcome you wish.

Question 20

How do we measure risk?

Answer 20

• we can measure risk of an asset by looking at the standard deviation of its returns
• standard deviation is a measure of how spread out those returns are. Its symbol is o (the Greek letter ‘sigma’)

Question 21

Reducing Risk through diversification

Answer 21

• diversification reduces risk by replacing a single risk with a large number of smaller, unrelated risks.
• the idea is to try to create a diversified portfolio of assets whose returns are NOT closely related (in statistics-speak, they are “not highly correlated”
• in practice, we want to have some securities whose price goes up in good times (in an economic expansion) and some that don’t go up as much (or even go
*down *) during expansions.
• and the same is true when we are in a recession.

• these returns average out, so the portfolio is likely to earn a return in the middle more consistently than any of the assets it contain.
• the idea of portfolio allocations is to earn a consistent return, with reduced risk -> not to squeeze every last nickel out of your investments.

Question 22

Diversification can’t solve everything

Answer 22

But be careful ..
diversification can’t solve everything!
• diversification can reduce firm-specific risk, which affects only a single company.
o firm-specific risk is also called “unsystematic risk.”
• diversification cannot reduce market risk, which affects all companies in the stock market.
o market risk is also called “systemic risk” -> risk of a market meltdown

Question 23

The trade off between Risk and Return

Answer 23

• there is a tradeoff between risk and return: riskier assets pay a higher return, on average, to compensate people for the extra risk of holding them.
o I would put it this way: investors demand a higher expected return from risky assets to compensate them for the higher risk
o with stocks, we call this difference between risky and risk free assets the “equity premium.”
o there is evidence that this should not exist . .. but it does.

• the equity premium is real: riskier assets pay a higher return, on average, to compensate for the extra risk of holding them.
• for example, over the past 200 years:
o average real return on stocks = 8%.
o average real return on government bonds = 3%.

Question 24

What is Stock Valuation?

Answer 24

Deciding whether to buy a company’s stock, you compare the price of the shares to the value of the company.
• if share price > value, the stock is overvalued.
• if price < value, the stock is undervalued.
• if price = value, the stock is fairly valued.
The key is to figure out the stock’s value!!!
One crude method is to calculate the stock’s discounted cash value.
DCV is one of many models that people use to try to determine value.

Question 25

Is the stock market “efficient”? The Efficient Markets Hypothesis

Answer 25

•Efficient Markets Hypothesis (EMH): theorizes that each asset price reflects all publicly available information about the value of the asset.
• at any instant, current prices reflect all the information available about the stock.
• if so, then the best estimate of value is the current price.

Question 26

Implications of EMH

Answer 26

1. Stock market is informationally efficient -> stock prices reflect all available information about the value of companies. This is violated if someone has inside information.
2. Stock prices follow a random walk -> a stock price only changes in response to new information (“news”) about the company’s value. News cannot be predicted, so stock price movements should be impossible to predict.
3. It is impossible to systematically beat the market -> by the time the news reaches you, investment professionals will have already acted on it. And it’s even hard for pros to beat the market.

Question 27

One way to invest…

Answer 27

Through mutual funds

Question 28

There are also differences between how investment pros manage the funds

Answer 28

• index funds - passively managed. Your profit is based on what the targeted index produces.
• managed funds - a real
person tries to pick the best investments.

Question 29

Managed funds

Answer 29

• a managed fund relies on a professional’s expertise to make stock choices.
° can be good, but hard to be consistently good over time.
Remember the Efficient Markets Hypothesis?
• an example of a good one is the Fidelity Contrafund.

Question 30

Index Funds

Answer 30

• an index fund is a mutual fund that buys all the stocks in a given stock index and just lets them sit there -> the S + P 500, MSCI EAFE, Russell 2000, etc.
o most famous example -> Vanguard S & P 500 Fund:
$805 billion in assets.

Question 31

Which is better? An index fund or a managed fund?

Answer 31

• the efficient market hypothesis implies that returns on actively managed funds should not consistently exceed the returns on index funds
o in any given year, an actively managed fund may outperform its index
o but over time, it will revert to the mean.

Question 32

It’s a simple choice…

Answer 32

• it costs more to invest in an actively managed fund (because you’re paying for the fund manager’s brain and work effort)
o and there is LOTS of evidence that, on average, they don’t produce better results!
• EMH says, “buy the index.”