This lesson introduces uncertainty, default, and risk. The methods for calculating expected returns and risk are introduced, and also how to adjust a rate of return to include default risk. Finally, credit agencies are introduced. 
 Expected returns  average returns given various outcomes
 Similar to an average or mean
 Promised returns  what company says will pay in the future
 Expected returns are always lower because of loan defaults or bankruptcy
 Return becomes a random variable
 Random variable  variable has various outcomes and each outcome has a probability associated with it
The Expected Return is:
Example 1 
Outcome (x) 
Probability (p) 
10 
0.4 
14 
0.2 
8 
0.2 
20 
0.2 

1.0 
Note  the probability always sums to one, because all outcomes are included. Moreover, all probabilities lie between zero
and one.
The variance is how spread out the outcomes are around the expected return
Standard Deviation is how spread out the outcomes are around the expected
return
 Reward is the expected return of an investment
 Risk  the variability of the expected return
 Measured by the standard deviation
 Variance  the units are squared
 Standard deviation  the same units as the expected returns
Example 2 
Outcome (x) 
Probability (p) 
90 
0.5 
80 
0.3 
105 
0.1 
30 
0.1 
Expected rate of return is 82.5, variance is 356.25, and standard deviation is 18.87
 Investors can be defined as
 Risk neutral  neutral between a sure bet and an expected bet if both are the same
 Indifferent between taking $100 as a sure bet or $100 if 50% chance he receives $200 and 50% he receives $0
 Risk averse  investors always takes the sure bet
 An investor prefers taking $100 as a sure bet as opposed to $100 if 50% chance he receives $200 and 50% he receives $0
 Risk taker  Investor takes the gamble for the higher payoff
 An investor prefers taking $100 if 50% chance he receives $200 and 50% he receives $0 as opposed to taking $100 as a sure bet
In this class, all calculations are risk neutral, because they are easier to calculate

 Default  when borrower does not pay back loan and/or interest:
 Bankruptcy
 Financial problems
 Credit risk
Example of default risk  you give a loan to a person for $400 and he promises to pay you back in one year at 10% interest
Outcome 
Outcome (x) 
Probability (p) 
Expected Return 
Pays loan on time 
$440 
0.8 
10% 
Pays half of loan 
$200 
0.1 
50% 
Defaults 
$0 
0.1 
100% 


1.0 

What is expected return of loan?
Expected payment amount is $440 (0.8) + $200 (0.1) + $0 (0.1) = $372
What is expected return of loan? Expected return is
Similar to the last lesson, you compare your return to a comparable U.S. government security and add a default premium to the loan
If a comparable oneyear Tbill is 3%, you should expect a higher rate of return.
Outcome 
Outcome (x) 
Probability (p) 
Expected Return 
Pays loan on time 
$400 (1 + r) 
0.8 
??? 
Pays half of loan 
$200 
0.1 
50% 
Defaults 
$0 
0.1 
100% 
What if we wanted an expected rate of return of 10%
Substitute $440 into the expected payment amount
You would charge your friend 31.25% interest. The default premium is 31.25%3% = 28.25%
All debt is financed by a combination of equity and loans

 Two credit agencies for corporations:
 Moody's
 Standard and Poor's
 Note  there are other credit agencies
 Divide corporations into two classes
 Investment grade
 Probability of default is less than 3%
 Speculative grade (or junk)
 During recession, default are 10%
 During economic booms, defaults are 1.5%
Investment Grade 
Moody's 
Standard & Poor's 
Exceptional 
Aaa, Aaa1, Aaa2, Aaa3 
AAA, AAA,AA+ 
Excellent 
Aa, Aa1, Aa3, Aa3 
AA, AA, A+ 
Good 
A, A1, A2, A3 
A, A, BBB+ 
Adequate 
Baa, Baa1, Baa2, Baa3 
BBB, BBB, BB+ 
Speculative Grade (Junk) 
Ba, Ba1, Ba2, Ba3 
BB, BB, B+ 
Poor 
B, B1, B2, B3 
B, B, CCC+ 
Very Poor 
Caa, Caa1, Caa2, Caa3 
CCC, CCC, CC+ 
Extremely Poor 
Ca, Ca1, Ca2, Ca3 
CC, CC, C+ 
Lowest 
C 
C 

FOLLOW ME