1. Investment REturns
Andras Bohak 10/14/2016

2. What is value? Is the projector in this class room valuable?
Would you be happy to have it if lost in the Sahara?
And a glass of water?
Then why is it so cheap?
Value is NOT an intrinsic property of things like shape or color
Nothing is valuable by itself
Something is only valuable if it is in the right hands in the right time
„Sport/science/culture/peace is important.”
Neither is
They might be for some people at some specific time and situation

3. Trade Trade is just like manufacturing
Orders things to a more valuable state
Trade can increase total richness
Common mistake: „If I earn return on the market, someone had to lose that money.”
Not necessarily. The cake we cut is growing!

4. Returns

5. Risk free return
Why do we expect any return on a risk free investment?
Positive time preference
Inclination of a consumer towards current consumption (expenditure) over future consumption
We miss effects of general development
Long term risk free real rate is usually 2-3%
Considerably lower today
How to approximate?
No credit risk: very safe government debt only
No inflation risk: inflation protected bonds (TIPS)

6. Risky return Risk = actual return may deviate from expected return
Why do we expect to get more return if we bear more risk?
Risk aversion
To quantify risk, we need
Possible outcomes
Possibilities
We can observe only one state of the world
What if we say today that expected return is +10%
But actual return turns out to be -5%
Did we make a mistake? We will never know
You can not tell if a dice is fair if you can roll it only once
In practice, we roll different dices once (e.g. returns for different months) and pretend those to be multiple rolls of the same dice
i.e. future return distribution

7. %: -5%
%: +10%
40%: +20% ret.

8. We are bad at risk... Tails: I pay you $100 Heads: You get nothing
How much do you pay for playing once? And a thousand times?
H: 100K USD payout with 10% prob
L: 10K USD payout with 90% prob
If the first tail is the nth then I pay you 2n dollars
Prob of first tail on the nth: 1/2n

9. Normal distribution Risk Expected return: Deviation from the mean
Standard deviation
Normal distribution
Effect of many small random
Central limit theorem
„real randomness”
Expected return:

10. Risk measures
We think that actual returns are combined results of small independent random events
Normal distribution
A natural risk measure is the standard deviation

11. More money is always better...
Risk aversion
MU(F)
MU(W)
W, F
U(W)
U(F)
More money is always better...

12. U(F)

13. 117 F1 F0 U1 U2 U3 U4 U5
Indifference curves

14. E(F1) F0
117
1+E(r) A B =
/(1+E(r))

15. 117
E(F1) F0 U1 U2 U3 U4 U5 U6
1+E(r) =
*(1+E(r)) B A

16. E(F1) T
E(F1D) S
E(F1C) R
E(F1B) Q
E(F1A) F0
F0A
F0B
F0C
F0D

17. E(F1) U6 U5 T Q U4 U3 R
1+E(r) U2 S U1 F0

18. E(F1) T U6 Q U5 Q C U4 T U3
1+E(r) U2 U1 F0

19. E(F1) U5 T U4 C Q U3
1+E(r) U2 U1 F0

20. E(F1) T Q R S F0