Career Knockouts and Risk Preferences

Article Quant Q&A · Author: Enrico

Summary

This discussion examines a simulation inspired by Mark Spitznagel’s account of traders choosing between strategies with different payoff shapes. One strategy offers frequent small gains and rare large losses; the other offers frequent small losses and rare large gains. The author attempts to give both strategies the same geometric growth rate, then asks how a job-loss threshold affects career survival and expected personal payout. The proposed simulation tracks wealth over time, stops a trader after a threshold breach, and compares survival duration and payout across strategies.

The central modeling question is how to represent a trader who can change strategies. The post does not resolve that question or provide simulation results. Its code keeps the selected strategy fixed and applies the knockout to an individual period’s return, so it does not establish that this matches the cited model’s career-level incentives. The discussion is useful as a framing of path dependence and incentive effects, but the implementation and interpretation remain tentative; the author is explicitly asking how to build and evaluate the simulation.

Key ideas

The post contrasts strategies with frequent small gains and rare large losses against strategies with the reverse payoff pattern.
It attempts to equalize the strategies’ geometric growth rates before comparing their outcomes.
A knockout rule can make career survival and personal payout depend on the sequence of returns.
The proposed code fixes strategy choice and applies the threshold to a single-period return.
The post leaves open how to model strategy switching and whether the implementation reflects the cited argument.

Tags

Statistics Risk management Backtesting Position sizing

Full text

# Wall Street Gambling Madness: a Simulation


# Wall Street Gambling Madness: a Simulation












In "The Dao of Capital" by Mark Spitznagel, at pag. 162, the author mentions at a computer simulation to understand what drives the Wall Street's gambling madness. I would like to it set up.

In presence of a profit level to reach to keep the job, or else being knocked-out:

> Traders with knockouts favored the huge infrequent risks - thus providing very likely career survival - whereas traders without knockouts avoided them.

In my code the traders can't change strategy because it is fixed. Contrary, if I understand correctly the author, they should be able to change it. Anyway, if I calculate the average number of periods for a trader "not knocked out" and the relative average payout when knocked out I can obtain similar conclusions.

Again, about the strategy change/preference:

> Moreover, lessening or removing the free option (meaning [...] share losses) had no effect on strategy preference. (Preferences were based on maximizing a trader's expected personal career payout; the statistical significance in this switch between strategy preferences was above 99 percent, with no sensitivity to the magnitude of each strategy's skewness nor profit and loss participation)

How can I manage the "maximization of the trader expected personal career payout" to introduce a "strategy change"? Does this just mean to simulate, and then to interpret, and see which strategy gives the greater expected payout when "knocked out"?

Basically, How would you implement the simulation stated by the author? Do you think it could be close to what I implemented?

Let me know if more details are needed. Thanks.

In the code below I'm trying a first simple attempt with only 2 discrete strategies, one with infrequent large losses and frequent small gains and an opposite one. Both have the same geometric averages as stated by the author.

```
# strategy 1: freq small gains and infrequent large losses
p1=9/10
g1 = 1.11
l1= 0.5

# strategy 2: freq small losses and infrequent large gains
p2=1/10
l2=0.9

# determine gain of strategy 2 to have same geometric mean as strategy 1
exp((p1*log(g1)+(1-p1)*log(l1) -(1-p2)*log(l2))/p2) -> g2

# check geometric means
p1*log(g1)+(1-p1)*log(l1)
p2*log(g2)+(1-p2)*log(l2)
g1^p1*l1^(1-p1)
g2^p2*l2^(1-p2)

# Expectation by wagering 1 on each strategy
p1*(g1-1)+(1-p1)*(l1-1)
p2*(g2-1)+(1-p2)*(l2-1)

# simulation
N = 100 # periods
B = 1e3 # bootstrap replicates

# knockout threshold, applied to the strategy return (is it correct?)
th = 1.1

# Control parameters
s1 = T # if True you are using strategy one
ko = T # If True you are inserting a profit level to knock out (out of the job - zero payout from that period to last N)

output = matrix(0,B,N)
output[,1]=1

for(i in 1:B)
{
  continue = TRUE
  n = 1
  while(n < N & continue)
  {
    if(s1)
    {
      r = ifelse(runif(1)<=p1,g1,l1)
    }
    else
    {
      r = ifelse(runif(1)<=p2,g2,l2)
    }
    
    if(ko)
    {
      if(r<th)
      {
        # knocked out
        continue = FALSE
      }
      else
      {
        output[i,n+1]=output[i,n]*r
      }
    }
    else
    {
      output[i,n+1]=output[i,n]*r
    }
    n = n+1
  }
}

# mean payout at last step
mean(output[,N])

# mean number of periods not knocked out
mean(apply(output,1,function(x) max(which(x>0))))

# mean payout when knocked out
mean(apply(output,1,function(x) x[max(which(x>0))]))
```

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Career Knockouts and Risk Preferences in Trading Simulations

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