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I am finding the evidence or reference saying that GameStop is a lottery-like stock but I could not find that.

What I did find so far is:

Hasso, 2021 documented that

GameStop investors had a history of investing in lottery-like stocks prior to investing in GameStop

Siong Tang 2021 documented that "GameStop has high volatility", which is a criteria of a lottery-like stock.

(Lottery-like stock is the stock that has both high volatility and high skewness)(Han, 2021)

But there is no paper that says GameStop is a lottery stock so far from my search, could you please provide me one(s)?

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I would argue that Game Stop is not a lottery-like stock. Or, if you would prefer, all stocks are lottery-like stocks.

The technical term for the payouts and associated probabilities for any asset is a lottery. From a technical perspective, a certificate of deposit is a lottery because while the FDIC guarantees the principal it does not guarantee the interest.

On the flip side, there is a tendency to use lottery-like or speculative when the prices do not reflect the long-run present value of future cash flows.

I would say the size of the dispersion term in the security is not, by itself, sufficient to make a security speculative. Let me give you an example, although it would be a poor example to compare Game Stop to.

Imagine two brothers married two sisters. They both bought homes at the same time. They purchased corner lots cattycorner from one another. The homes were built by the same builder with identical materials. They are the same in all respects. We will treat the deeds of the homes as securities.

The two families each had one child. They grew up and moved away. The couples, who had always loved doing things together, were killed in a tragic accident. They both left their homes to their one child.

Although their homes were identical, the rest of their lives were not. Gerald's parents were very frugal and careful. They built up a local real estate empire. Agatha's parents lived life in the moment. Although they had a small annuity that passed to Agatha, the home was all they had.

The two cousins agreed that they wanted to put their homes up for sale. Both had built lives for themselves in their respective cities and although sad, hired a realtor to get rid of the homes.

The realtor advised Gerald that putting many of the remaining rental properties on the market at once would quickly depress the market. They would have to be sold slowly.

Both homes sold almost immediately for $100,000. However, a week before closing, the family buying Gerald's home died in a terrible automobile accident leaving no assets causing the sale to fall through.

Gerald, who had come into town to sign any documents and take one last look, was sitting in a bar. He was talking about his money problems and how he needed cash fast and how he needed to unload the home immediately. As it happened, a bar patron named Patrick said he would purchase the home but he could only pay $70,000 because that was all he had in his bank account.

Gerald needed money for estate taxes, to repair properties, and to pay other obligations so he took the offer. Patrick actually had $100,000 in his bank account.

Agatha sold her home to Lily. Lily had been saving up and also paid entirely in cash. Agatha received \$100,000 at closing while Gerald received \$70,000. By chance, the homes closed on the same day at the same time across the hall from one another at the same attorneys' offices. This begins our time series for identical assets.

Patrick paid \$70,000 at time zero while Lily paid \$100,000 at time zero.

As fate would have it, both Patrick and Lily worked at the same factory. Realizing the homes were identical, they split all costs for repairs, changes and so forth.

About nine months into the year, the factory that they worked at announced a planned expansion. That drove up housing prices in the area. Out of curiosity, the two homeowners split the cost of having an appraiser come and look at their home on their one-year anniversary. The homes were appraised at \$110,000.

Patrick's time series is now $\{\\\$70,000;\\\$110,000\}$ while Lily's is $\{\\\$100,000;\\\$110,000\}.$ They both decide to keep their homes, although a speculative purchaser does come by and offer them the appraisal amount. Instead, a third identical home on the street was sold for that amount of money.

Nine more months pass and the factory announced an embezzlement that was causing it to reduce its workforce. Both Patrick and Lily were being laid off and real estate prices fell.

Both homeowners put their homes on the market because they both had job offers out of town. They both received \$90,000 for their homes, by happenstance, the closing was on their two-year anniversary.

Patrick's time series is now $\{\\\$70,000;\\\$110,000,\\\$90,000\}$ while Lily's is $\{\\\$100,000;\\\$110,000,\\\$90,000\}.$ Additionally, Patrick still has another \$30,000 that remained unused and sitting in a bank account. It had earned 3% per year for each year compounded annually.

If we only look at volatility, then Patrick's home prices were four times as volatile with a price variance of \$400,000,000 and a corresponding standard deviation of \$20,000 compared to Lily's \$100,000,000 variance with a standard deviation of \$10,000; twice as volatile in a standard deviation space.

Even when looked at from a cash flows perspective and ignoring the intervening unrealized offer price, there is greater volatility in Patrick's home. From a variance perspective, Patrick's home is the riskier home. However, the homes are physically identical and have identical replacement costs.

Now let's look at this from a portfolio perspective.

With the savings account, Patrick's time series is $\{100,000;140,900;121,827\}$. His portfolio standard deviation is \$20,465.45 and variance is \$418,834,543.00. When you include his risk-free asset, his measured variance and standard deviation went up!

Now let us think about risk again. If we define risk as exposure to loss, Patrick placed less money at risk and had a higher binomial probability of hitting any goal state with a lower binomial variance. Any reduction in the denominator of a return equation reduces the risk of goal failure because when you divide the numerator by an increasingly small number, the ratio goes up and the percentage mass on the other side of the goal state increases. If your utility function were succeed or do not succeed then any reduction in price for equal value reduces risk and increases the probability of being in the goal state.

Variance is only valid when an asset is in equilibrium and only if the distribution has a defined second moment.

Before we get back to Game Stop, let us add one more observation about risk.

Let us assume that my wife and I just purchased a Power Ball ticket and we define risk as exposure to uncertainty. Was that Power Ball ticket a risky purchase?

Clearly, the answer is "no." There is almost no uncertainty at all. I am almost perfectly certain that I am going to lose. If there was a lot of uncertainty, I would hire an accountant, an attorney, a trust officer, and a social secretary. I am certain to lose; the state is certain to win, well, almost certain.

The variance is roughly $300,000,000^{-2}\approx{10^{-17}}$. That is, basically, zero.

Likewise, it is a risk-free asset to the state that issues it as well. Both parties are at no risk of loss. I will almost certainly lose and the state will almost certainly gain. States love assets like that.

Now back to Game Stop. In the long run, it isn't worth that much. As I would pay less than book value before I considered it, that is a reduction of over 20 times its current price. That would drive my risk of loss down. If the only concern were the long-run value, then my certainty of loss is very very high.

Conversely, if my only concern were long-run value, then shorting it would be wise. Of course, I would need very deep pockets to avoid being destroyed by such an action. The long run may be much longer than I am alive.

This security is shorted roughly 4:1 at the moment. It's price is very fragile because it could easily be subject to margin calls. In the short run, it may be worth much more than this or much less. I am not interested enough to value it on that basis as that is a lot of work for something that I do not care about.

However, using the above two examples, you can start asking how elastic this security's price is. You can look at the drivers such as liquidity costs and social media. It is possible, though exceedingly difficult, to model this security.

From there, you can determine if you are paying one hundred thousand for the house, seventy thousand for the house or two hundred thousand for the house.

Risk is not just dependent on the historical volatility. Your risk depends on your price as well as collateral to support your choices, time frames, and so on. It also depends on the chance the house will burn down. In our illustration, it did not happen but it could have. You cannot ignore the possibility of Game Stop ceasing to exist.

For the state issuing a Power Ball ticket, there is almost no risk. Is lottery the correct term?

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  • $\begingroup$ Thanks @Dave, I face it from your answer " If we only look at volatility, then Patrick's home prices were four times as volatile with a price variance of 400,000,000 and a corresponding standard deviation of 20,000 compared to Lily's 100,000,000 variance with a standard deviation of 10,000; twice as volatile in a standard deviation space.". I am wondering what does "Patrick's home prices were four times as volatile with a price variance of 400,000,000" mean?, and what is price variance then ? What is variance perspective in your example? Is this the square of std. dev. in math? $\endgroup$ Nov 3, 2021 at 3:39
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    $\begingroup$ Yes. The variance, generally, is the square of the standard deviation. Just a technical note, those numbers are from Excel. To be very technical, the unbiased estimator of the variance is not the square of the unbiased estimator of the standard deviation. Excel does not provide a correct unbiased estimator of the standard deviation. You could multiply all the standard deviations by the square root of pi divided by two if you wanted a correct, unbiased estimator. $\endgroup$ Nov 3, 2021 at 5:58
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    $\begingroup$ @Louise this answer treats an asset as having its own data generating parameters or population parameters. It is true that such a perspective is a bit artificial but finance does that regularly. There is more than one type of common share for Unilever with equal claims and powers over the firm, yet we treat them as two different objects. I am really making a point about blindly using tools. Models like the CAPM assume that all markets in the world are in equilibrium, not just financial markets. The lessons do not hold automatically if that isn't true. $\endgroup$ Nov 3, 2021 at 6:01
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    $\begingroup$ @Louise I only considered the variance of the price because returns are a ratio of prices. Under mild assumptions, they would have to have fat tails and could not possibly have a mean or a variance. Under mild assumptions, the ratio of prices would be the ratio of normal distributions. There are two ways to model that with different parameterizations. Either it is a Cauchy distribution, modified by the risk of fire damage, or it is a mixture of a finite variance distribution and a Cauchy distribution. I didn't want to go there. $\endgroup$ Nov 3, 2021 at 6:03

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