Formulas

Question 1

Answer 1

Constant Growth Dividend Discount Model (DDM)/ Intrinsic Model

=calculates the value of a dividend paying security w/a constant growth rate in $ terms

= it is used to predict the $ of a stock based on the theory that it’s present day price is worth the sum of all it’s future dividend payments, discounted to now

D₁ = next year’s dividend

r=investor’s required rate of return

g= dividend growth rate

Present value of future dividends > current MV of stock = undervalued
Present value of future dividends < current MV of stock = overvalued

Question 2

D₁

Answer 2

D₁ = D₀(1+g)

Question 3

Answer 3

Taxable Equivalent Yield

= provides the return that is required on a taxable investment to make it equal to the return on a tax-exempt investment

r=nominal rate of return

t= investor’s marginal tax rate

Question 4

Answer 4

Jensen’s Performance Index/ Alpha

= measures the performance of a portfolio manager relative to the performance of the market.

=if the value is (+), then it is earning excess returns. They “beat” the market.

⍺_p=difference of return from the amount required by investors

r_p=return of the portfolio

r_f=risk free rate of return

r_m=return of the market

β_p=beta of the portfolio being measured

Question 5

Answer 5

Treynor Ratio

=measures risk-adjusted performance of a portfolio manager

=reward to volatility ratio

r_p=return of the portfolio

r_f=risk free rate of return

β_p=beta of the portfolio being measured

It is used comparatively, so you have to compare 2+ investments for it to be useful. The higher the #, the better.

Question 6

Answer 6

Taxable Equivalent Yield

=provides the return that is required on a taxable investment to make it equal to the return on a tax-exempt investment

r= nominal rate of return

t=investor’s marginal tax rate

Question 7

Answer 7

Sharpe Ratio

=measures risk-adjusted performance of a portfolio in terms of standard deviation

=adjusts a portfolio past performance or expected future performance for the excess risk that was taken by the investor

r_p=return of the portfolio

r_f=risk free rate of return

σ_p=standard deviation of the portfolio being measured

Assumes investment returns are normally distributed. It is comparable, the higher the better.

Question 8

R² is more or less than .7?

Answer 8

If less than, use Sharpe (not sufficiently high enough)

If greater than, use Treynor (sufficiently high enough)

Question 9

Answer 9

Capital Asset Pricing Model (CAPM)

=used to determine a theoretically appropriate required rate of return for an asset

=it describes the relationship between systemic risk and expected return for assets.

=regularly used for pricing risky securities and generating expected returns for assets given the risk and cost.

r_i= investor’s required rate of return

r_f= risk free rate of return (T-Bill)

r_m= return of the market

β_i=beta of the security being measured for the required return

(r_m - r_f) = market risk premium

Question 10

What are comparative values?

Answer 10

Sharpe Ratio

Information Ratio

Treynor Ratio

Question 11

Answer 11

Covariance

=measures how one security behaves as a direct result of another

+ means they move together, - means they move apart

⍴_ij= correlation of securities i and j

σ_i= standard deviation of security i (or j)

Even if we know they move apart or together, we don’t know how much

Question 12

Answer 12

Expected Rate of Return

=the rate an investor should expect based on the price paid for a security

D₁= next year’s dividend

P= market price paid for security

g= dividend growth rate

Always find D₁. We are usually given D₀, which is this year’s dividend

D₁ = D₀(1+g)

Question 13

Answer 13

Beta

=provides risk as a measure of volatility relative to that of the market

=measure of systemic risk

σ_i= standard deviation of an individual security

σ_m= standard deviation of the market

⍴_im= correlation between an individual security and the market

COV_im= covariance between an individual security and the market

The market/benchmark is always assumed to have a beta of 1.0

• ~1.0 = similar performance to the market
• <1.0 = less volatile than the market
• >1.0 = more volatile than the market

Question 14

Answer 14

Change of a Bond Price

= states the change of a price that will occur in a bond as interest rates change

△P = $ change in price

P = price of a bond

△P/P = % price change of a bond

-D = the duration in terms of years used as a (-) value

△_y = % change in interest rates. If they decrease, this # should be a (-)

y = Years to Maturity

Question 15

Which ratio measures total risk?

Answer 15

Sharpe ratio, because it defines risk in terms of standard deviation including both systematic and unsystematic risk

Question 16

Current Yield

Answer 16

=annual income expected, generally from a bond

Annual interest in dollars

____________________

Bond’s market price

Question 17

Property’s intrinsic value

Answer 17

=helps determine the value of an investment property

Net Operating Income (NOI)

market value = ______________________

Capitalization Rate

Cap rate = required rate of return taking things into account like type, location, age, quality of tenants, etc

Question 18

Intrinsic value of a call option

Answer 18

= Determines how in the money an option is, or how much profit currently exists

Market Price - Exercise Price

If the calculated value is negative, the IV is ZERO

Question 19

Intrinsic value of a put option

Answer 19

= Determines how in the money an option is, or how much profit currently exists

Exercise price - market price

If the calculated value is negative, the IV is ZERO

Question 20

Real rate of return

Answer 20

AKA: inflation-adjusted return

=annual percentage of profit earned on an investment, adjusted for inflation

1 + Nominal Rate

_______________ - 1

1 + Inflation Rate

Question 21

Tax-Exempt Yield

Answer 21

= the interest rate on a taxable security that would generate an equivalent yield on a tax-exempt yield.

Tax-Exempt Yield = taxable yield x (1 - tax rate)

Question 22

Dividend Payout Ratio

Answer 22

=the percentage of earnings paid to shareholders via dividends

Dividends paid

_____________

EPS (earnings per share)

Question 23

Stock/Dividend Yield

Answer 23

=The dividend yield compares the amount of the dividend paid to the share price of the company’s stock.

Dividend per share

________________

Stock price per share

Question 24

Margin Call

Answer 24

=Margin calls are demands for additional capital or securities to bring a margin account up to the minimum maintenance margin.

1- Initial margin percentage

___________________________ x Purchase price of stock

1 - Maintenance margin percentage

Question 25

P/E Ratio

Answer 25

=helps determine if a stock is over or under valued

=the dollar amount an investor can expect to invest in a company in order to receive $1 of that company’s earnings

current market price

________________

earnings

Question 26

What are examples on the calculator for using annuity due?

Answer 26

This is begin mode!

• Cash Outflows
  
  • payments to colleges
  • retirement income
  • gifting
  • insurance premium payments
• Cash Inflows
  
  • SS benefits
  • pensions
  • retirement planning
  • disability

Question 27

With NPV calculations, what result is yes and no?

Answer 27

NPV= uneven cash flows.

(+) = yes, do investment

(-) = no, don’t do it

Question 28

NPV vs IRR

Answer 28

• NPV is superior because:
  
  • it is more reasonable to invest at the required rate of return than IRR
  • With changes of more than 2 in/outflows in an investment project, there is only one NPV, but multiple IRRs
• IRR is typically sued for fixed income