Ukrainian IT sector – one of those least sectors which maintained its growth in

2010-2014 period

Investment activity overview

The approach which uses industry information in order to gain future performance information

Market volume

Type of industry

Number of employees

Initial

investments

LocationNumber of competitors

Probability and return of :• Failure• Break even• Success

Typical milestones of venture industry company

Prototype creation

Successful prototype testing

Successful sales and high market share

  Start of sales IPO

The main problem

‘’ How using the information about the probabilities of success/break even/failure and corresponding returns define the sum to invest on each milestone?’’

Applications of Kelly criterion

Stock market Black jack Sports betting

2 types of Kelly criterion

𝑓 =𝑝𝑏−𝑞𝑏

“Bookmaking” criterion

Classical criterion

p – probability of successq – probability of failureb – is the net odds received on the wager ("b to 1”)f – Kelly proportion of capital

Example. Description1st project :

• with probability 40% won’t

bring anything

• with probability 35% will

bring x1.1 of costs invested

• with probability 25% will

bring x7 of costs invested

2nd project:

• with probability 30% won’t

bring anything

• with probability 40% will

bring 1.12 of costs invested

• with probability 30% will

bring x6 of costs invested

Capital : 40 000 000 $

Each project has 3 milestones:0 – the beginning1 – intermediate step2 – final step

Markowitz approachUsing Marcowitz criterion with risk aversion coefficient which

equals 7 we have next results:

1st project : 1 502 700$ 2nd project : 2 057 000$

Rest of sum should be invested into cash(non-risk asset)

Kelly approach. Step 1Using «bookmaking» Kelly criterion we need to find the proportions of a capital which should be invested into projects:

1st project : 5 000 000 $2nd project : 6 400 000 $

Kelly approach. Additional information

Consider that we have received the next piece of information:

Now we need to use classical Kelly criterion in order to define the proportions of 5 000 000 and 6 400 000 which we need to invest on each of milestones.

Project 1 Project 2

From 0 to 1 80% 90%

From 1 to 2 53% 80%

Kelly approach. Step 2

Project 1 Project2

From 0 to 1 1 400 000$ 4 257 000$

From 1 to 2 192 000$ 3 831 000$

Overall 1 592 000$ 8 088000$

Results comparison

Marcowitz Kelly0.00

5000000.00

10000000.00

15000000.00

20000000.00

25000000.00

Standart deviation

Marcowitz Kelly0.00

2000000.00

4000000.00

6000000.00

8000000.00

10000000.00

12000000.00

14000000.00

Mean

Marcowitz Kelly0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mean/standrart deviation ratio