Title: Public vs Private Investments Author: Thomas Breuel Institution: UniKL
Previously:
In the manufacturing simulation, we had:
The result:
Investments:
Setting:
Simplifications:
N = 10
# uncertainty = 0.3*abs(randn(N))**.5
uncertainty = linspace(0.1,0.7,N)
uncertainty = numpy.sort(uncertainty)
plot(uncertainty)
[<matplotlib.lines.Line2D at 0xd7c0f10>]
For private investors, the entire benefit (return on investment) accrues to the investor.
This means that investors making good decisions will have more money to invest next time.
wealth = ones(N)
wealth_over_time = []
frac = 0.5
for y in range(50):
M = 15
yields = randn(M)*0.3
predicted = yields[:,newaxis] + randn(M,N)*uncertainty[newaxis,:]
selected = argmax(predicted,axis=0)
wealth = (1.0-frac)*wealth + frac*(1.0+yields[selected])*wealth
wealth_over_time.append(wealth.copy())
wealth_over_time = array(wealth_over_time)
for i in range(N):
plot(wealth_over_time[:,i])
Observations:
A second model of investments is public investments.
Here, a set of experts are given an annual budget to invest in the market based on their yield predictions.
At the end of the year, all the returns on the investments are gathered together into a single budget and equally distributed again for next year.
wealth = ones(N)
wealth_over_time2 = []
frac = 0.5
for y in range(50):
M = 15
yields = randn(M)*0.3
predicted = yields[:,newaxis] + randn(M,N)*uncertainty[newaxis,:]
selected = argmax(predicted,axis=0)
wealth = (1.0-frac)*wealth + frac*(1.0+yields[selected])*wealth
wealth[:] = mean(wealth)
wealth_over_time2.append(wealth.copy())
wealth_over_time2 = array(wealth_over_time2)
Let us plot the total wealth generated by the two approaches.
plot((sum(wealth_over_time,axis=1)),color='blue')
plot((sum(wealth_over_time2,axis=1)),color='green')
[<matplotlib.lines.Line2D at 0xde2b0d0>]
Observations:
QUESTION
Why do we compare total wealth in the two schemes? What does that actually reflect?
With private investments, the best investors accumulate the wealth. Is this a good thing?
Attacks on public investors:
The public investement schemes are easy to attack.
QUESTION
Can you design a public investement scheme that mimics the success of the private investment scheme?
How can you make it attack proof?