Equations

Question 1

What is the equation to determine the price that will result in a margin call?

Answer 1

Solve for the Price at which the equity equals the maintenance margin MM = Maintenance Margin P = Price that will result in margin call S = # of shares L = Loan Amount MM = (S x P - L) / (S x P) Example: 100 shares purchased at 50 a share using 3,000 in cash and 2,000 in borrowed funds .25 = (100P - 2,000) / 100P .25(100P) = 100P - 2,000 25P = 100P - 2,000 2,000 = 75P 26.667 = P

Question 2

Annualized Interest Rate If an interest-bearing account is paying 1% per month, you get 1%*12 months = 12% interest per annum. Correct? No!

Second Example - Converting Monthly to Annual

As an example, consider the following: your current monthly interest rate on a loan where interest compounds monthly is a significant 2.5 percent.

Answer 2

First Example

1. Convert =
   
   1. 1% / 100 = .01
2. Add 1 =
   
   1. 1.01
3. Exponent
   
   1. 1.01¹² =
4. Subtract 1 =
   
   1. 1.1268 - 1 = .1268
5. Multiply by 100
   
   1. 12.68%
6. Annual Rate = 12.68%

Second Example - Converting Monthly to Annual

1. Convert =
   
   1. 2.5 / 100 = .025
2. Add 1 =
   
   1. 1.025
3. Exponent of 12
   
   1. 1.025¹² = 1.3449
4. Subtract 1
   
   1. 0.3449
5. Multiply by 100
   
   1. 0.3449 x 100 = 34.46%
6. Annual rate of 34.46%

Question 3

Dividend Discount Model

Answer 3

The Gordon growth model can be used to value a firm that is in ‘steady state’ withdividends growing at a rate that can be sustained forever

V = D₁ / (r - g)

1. D₁ = The value of next year’s dividend
2. r = the cost of equity capital (or the rate of return required)
3. g = the dividend growth rate

The dividend growth rate is the annualized percentage rate of growth that a particular stock’s dividend undergoes over a period of time.

Example

1. Determine Growth Rate with dividend payments to its shareholders over the last 5 years
   
   1. $1.00
      
      1. Growth Rate = N/A
   2. $1.05
      
      1. Growth Rate = $1.05 / $1.00 - 1 = 5%
   3. $1.07
      
      1. Growth Rate = $1.07 / $1.05 - 1 = 1.9%
   4. $1.11
      
      1. Growth Rate = $1.11 / $1.07 - 1 = 3.74%
   5. $1.15
      
      1. Growth Rate = $1.15 / $1.11 - 1 = 3.6%
   6. Average of these FOUR Annual Growth Rates: 3.56%
   7. Confirm average of these four annual growth rates using:
      
      1. $1 x (1+3.56%)⁴ = $1.15
2. Assume next year’s dividend will be $1.18 and the cost of equity capital is 8%, the stock’s current price per share calculates as follows:
   
   1. P = $1.18 / (8% - 3.56%)
   2. P = $26.58

Rational is Present Value

1. The rationale for the model lies in the present value rule - the value of any asset is thepresent value of expected future cash flows discounted at a rate appropriate to the riskinessof the cash flows.

Question 4

Required Rate of Return

R = (D₁ / P) + G

Answer 4

R = (D₁​ / P) + G

Required Rate of Return

1. $1.5 expected dividend
2. $29 price
3. 25% growth

R = (1.5 / 29) + .25

R = .3017

R = 30.17%

Question 5

Covariance

COV ij = Þ_ij σ_iσj

Answer 5

COV ij = Þ​_ij σ_iσj

1. Covariance of i and J is equal to
   
   1. the Correlation of i and j multiplied by
   2. the Standard Deviation of i mutliplied by
   3. the Standard Deviation of j,

Covariance

1. Find it?
   
   1. Calculate the mean (average) prices for each asset
      
      1. Example = Mean of S&P 500 = 2,044.80
      2. Example = ABC Corp. = 109.20
   2. For each security, find the difference between each value and mean price.
      
      1. S&P 2013 = (1,692 - 2,044.80) = - 352.80
      2. ABC 2013 = (68 - 109.20) = - 41.20
   3. For each time period (must keep the time period consistent), multiply the difference discovered in #2 above for each separate security.
      
      1. 2013 = 14,535.36
   4. Add the sum for each time period found in number 3, and divide by number of periods
      
      1. 34,429.20 / 5 - 1 = 9,107.30
   5. In such a case, the positive covariance indicates that the price of the stock and the S&P 500 tend to move in the same direction.
2. What is it?
   
   1. Covariance measures the total variation of two random variables from their expected values. Using covariance, we can only gauge the direction of the relationship (whether the variables tend to move in tandem or show an inverse relationship). However, it does not indicate the strength of the relationship, nor the dependency between the variables.

Correlation

1. What is it?
   
   1. On the other hand, correlation measures the strength of the relationship between variables. Correlation is the scaled measure of covariance. It is dimensionless. In other words, the correlation coefficient is always a pure value and not measured in any units.
2. Causation?
   
   1. Correlation must not be confused with causality. The famous expression “correlation does not mean causation” is crucial to the understanding of the two statistical concepts.
   2. If two variables are correlated, it does not imply that one variable causes the changes in another variable. Correlation only assesses relationships between variables, and there may be different factors that lead to the relationships. Causation may be a reason for the correlation, but it is not the only possible explanation.

Question 6

Real Rate of Return

calculate the real rate of return of the following: nominal return = 10% infaltion = 4%

Answer 6

Real Rate of Return = (1 + Nominal Rate) / (1 + Inflation Rate) - 1

Real Rate of Return = 1.10 / 1.04 - 1

Real Rate of Return = .0577%

Question 7

geometric mean

Answer 7

calculate the geometric mean of the following: returns: 15.2% 9.1% 6.5% 18.3% 16.8%

1. square root of the following: pv = -1 fv= 1.152 x 1.091 x 1.065 x 1.183 x 1.168 n = 5 pmt = 0 13.09%

OR

1. [(1 + r1) x (1 + r2) x (1 +rn) x … - 1]1/n -1
2. [1.152 x 1.091 x 1.065 x 1.183 x 1.168]^1/5 - 1
3. 1.1309
4. 13.09%