Measuring the Risk of Falling Below an Investor’s Initial Capital
Summary
The document considers an investor whose primary concern is whether portfolio value ever falls below the initial investment, even if the strategy later earns a positive return. It explains why variance, Sharpe ratio, maximum drawdown, and tail-loss measures such as VaR or CVaR do not directly capture that path-dependent preference: they do not specifically measure the worst cumulative return relative to the starting capital.
One proposed measure is the minimum cumulative return from the initial date to any point in the investment horizon. Its value represents the greatest interim loss relative to seed money, and an investor could seek a strategy with a favorable value at high probability. The answer also suggests dynamic risk taking that begins conservatively and increases after gains, while acknowledging uncertainty about practical performance. Another response frames the preference as a threshold rule and proposes exiting if portfolio value reaches the initial level. Neither response establishes a reliable way to guarantee against interim losses; the discussion highlights that certainty may be unattainable.
Key ideas
- The stated preference concerns whether cumulative wealth ever falls below initial capital.
- A minimum cumulative return over the horizon captures the worst interim loss from the starting point.
- Conventional dispersion and tail-risk measures do not directly encode this path-dependent threshold.
- Dynamic strategies may increase risk after gains, but their practical ability to protect seed money is uncertain.
- A stop-loss at initial capital is another proposed way to express the investor’s threshold preference.
Tags
Full text
# The best "risk measure" for an investor who does not want to lose any of his seed money
# The best "risk measure" for an investor who does not want to lose any of his seed money
### Question
- There is an investor who is afraid of losing any of his seed money (initial investment).
- Variance of investment returns is not a problem to him. He is willing to take variance as long as he does not lose his seed money.
- The investor is afraid of losing any of his initial investment, even a little. So even if he earns a lot at the end of investment period, if he has to go through losing any of his initial investment (seed money) during the investment, he would not like this investment plan.
- Which risk measure would be appropriate for this type of investor?
### Example
- Risk measures including variance, therefore, are not appropriate yardsticks for this type of investors. So I excluded variance, downside variance and sharpe ratios. ( I know sharpe ratio is a risk measure per se.)
- Maximum Drawdown seems to work, but whether seed money is being lost or not does not take into its account. As such, I am not sure if MDD is approrpriate.
- In the same sense, VaR and CVaR do not take into account the seed money
## Answer by fes (score 1)
https://quant.stackexchange.com/a/59204
As many have suggested in the comments, it might be hard, if not impossible, to find an investment that gives positive returns with certainty. However, you might consider a metric such as
$$R=\underset{s\in [0,T]}{\min}r_{0,s}$$
where $r_{0,s}$ is the portfolio return between the initial investment point $0$ and $s$. $R$ gives the highest share of seed money lost between $0$ and $T$. Then you could try to find an investment that with high probability has a good $R$.
You can affect $R$ through dynamic trading. As in this paper, the optimal strategy seems to increase risk after positive returns. So you would start investing in the risk-free asset and gradually increase risk after that. This way it might in theory be possible to guarantee positive returns for initial investment, though not sure how well this works in practice.
## Answer by develarist (score 0)
https://quant.stackexchange.com/a/59217
Since you yourself said the investor is willing to take variance/risk as long as she doesn't lose her seed money, then her objective function is not entirely a function of any risk measure describing some dispersion from a central tendency, neither the lower tail distribution. Instead, her objective function is a function of her cumulative returns being below $1$ at any point in time.
A risk measure is pointless for controlling such preferences and searching for one is totally missing the point (although you yourself did already rule out every possible risk measure out there so why keep asking?). Formulating an objective function with cumulative returns is pointless as well since cumulative returns are non-stationary and multi-modal.
All the investor can use is a perpetual stop-loss limit order that signals divestiture when portfolio price falls below the initial investment ("seed") price.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.