Investment REturns Andras Bohak 10/14/2016

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

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!

Returns

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)

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

0.000001%: -5% 59.999999%: +10% 40%: +20% ret.

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

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:

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

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

U(F)

117 F1 F0 U1 U2 U3 U4 U5 Indifference curves

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

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

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

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

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

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

E(F1) T Q R S F0