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Random Facts

I put random facts I find interesting in here, or something I want to remember.

Latency and A/B Testing​

A famous Amazon A/B test intentionally delayed page latency by 100ms and found even small delays (not noticeable by blink of an eye) can have substantial impact on user engagement and revenue outcomes. This is also an example of high elasticity, where demand is very sensitive to small factors. If a site slows just slightly, there's a big shift in the user response and behavior. Thus, there is a high elasticity of demand with respect to latency.

Elasticity​

Elasticity can be thought of as synonymous with sensitivity. Other economic examples of elasticity include price elasticity of demand where raising the price of a product like coffee by 10 cents can have dramatic reduction in the number of sales.

The mathematical formulation of elasticity is:

Price elasticity=%ΔQuantity Demanded%ΔPrice\text{Price elasticity} = \frac{\%\Delta \text{Quantity Demanded}}{\%\Delta \text{Price}}

For elasticity >1>1 it is elastic (sensitive), elasticity <1<1 it is inelastic (insensitive) and =1=1 it is unit elastic (proportional).

Free Cash Flow​

Recently the news of Oracle's stock rally read:

The biggest question for investors is how Oracle can continue funding that accelerating capex spend. Already, Oracle’s free cash flow in fiscal 2025 was negative for the first time in over a decade, as its executives doubled down on their cloud dreams. And despite the recent stock surge, Oracle might be reticent to issue more equity, considering it has been buying back its shares for years.

Free cash flow (FCF) is the amount of cash left over after paying for operating expenditure (opex) and capital expenditure (capex). If the free cash flow is positive, the company has spare cash left over to pay dividends, buy back stock, pay debt or make new investments. If the free cash flow is negative, the company does not have enough cash to cover all its expenses and need to find money via borrowing, issuing stock etc. to make those payments.

Issuing More Equity = Bad?​

Issuing stock is a way for companies to raise money, but at the expense of shareholders who see the value of their shares diluted.

The opposite of this is buying back stock which reduces outstanding shares. This increase Earnings Per Share (EPS) as profit is distributed over fewer shares. This also signals confidence to investors that they think the stock is undervalued and rewards investors.

Operating Income​

Operating income is the profit generated by a company after deducting cost of goods sold (COGS) and operating expenses (e.g. wages) from total revenue. It excludes non operating expenses like taxes, interest from loan payments, etc.

Operating Income=Total Revenue−COGS−Operating Expenses\text{Operating Income} = \text{Total Revenue} - \text{COGS} - \text{Operating Expenses}

For example, it is clear that Amazon's high margin cloud business AWS is their biggest money maker by looking at the percentage of operating income coming from cloud services.

Net Income​

You have Gross Income (revenue minus COGS) which is product specific, then Operating Income (minus operating expenses), then Net Income which is the bottom line profit after all expenses including interest and taxes are subtracted from revenue.

Net Income=Total Revenue−All Expenses\text{Net Income} = \text{Total Revenue} - \text{All Expenses}
Free Cash Flow vs. Net Income

Net income is revenue minus expenses and is at the bottom of the business' income statement as it is the money left from deducting all expenses. In accounting, since revenue is recorded when earned not necessarily received, and expenses are recorded when incurred, not necessarily paid, specific accounting methods and practices can easily change the net income number.

Free cash flow on the other hand is about cash balance and the money the business has after paying capex and opex. It is the cash inflow minus cash outflow. It does not involve non cash expenses like depreciation which is included in net income. The crucial difference here is that net income recognizes revenue when it is earned while FCF accounts for actual cash flowing in and out.

All this leads to the argument that free cash flow is a fact while earnings i.e. net income is an opinion. FCF is harder to manipulate than net income as it measures actual cash movement over accounting assumptions. Hence why FCF is most used rather than net income in considering whether a company is a good investment.

Vesting​

Think of vesting as a gift with strings attached (conditions to meet). For example with RSUs you are promised a certain amount of stock, but you only get them if you stay for long enough periods of time at the company. The first year you might get 250, then 500 the next, then 1000 the year after. If they are vested, it means that you've met the conditions and gained ownership over it. If they are not vested, you stand to lose them.

When RSUs are vested, they turn into actual shares of the company that you now own. This is treated by the IRS as income. This can be tricky because taxes are due even when you do not sell! Commonly companies will sell shares automatically to cover this i.e. withhold the taxes for you when vesting.

Stock Options​

Stock options differ from RSUs in that you get the opportunity to buy stock at a set price, aka the strike price. The strike price allows you to lock in the stock price at the current rate so that if the company does well in the future and the stock rises, you can buy the stock at the lower guaranteed rate and sell to pocket the difference. Note that it is not a discount upfront, you only earn money if the stock grows.

Employee stock options are a form of call options, but differ in that they are issued by the company itself and not tradeable, instead of being traded on the market.

Call Options​

Call options grant the right but not the obligation to buy a stock at a given price (the strike price) before a certain date i.e. the expiration date. On open markets, you must pay a premium to the seller to buy the call option.

Put Options​

Put options grants the right but not the obligation to sell stock at a given price, within a specified time period. This can be a good hedging strategy, say if you wanted to hedge against a stock which you currently own at $25 a share. With a strike price of $20, you know that if the stock falls precipitously, you can exercise the put option and protect yourself from any losses below $20.

Language & Grammar​

Subjunctive Clause​

The subjunctive clause which lacks inflection is used when associated with something hypothetical. It is used to express wishes, hypotheticals, suggestions, or demands.

Example:

It's crucial that he be here by noon.

I insist that he leave us alone.

Split Infinitives​

Split infinitives are when you squeeze an adverb between the "to" and "infinitive", e.g. to boldly go.

To boldly go where no man has gone before.

To patiently wait at the bus stop.

In informal settings, split infinitives are fine. In formal writing however, they should be avoided to promote clarity.

You can come up with varying examples of split infinitives that are objectionable:

It was unkind to in this manner treat their brother.

The advice is to avoid split infinitives if you are unsure of the audience, and only to rephrase or remove a split infinitive if it can be done without compromise (not an awkward or ambiguous rephrase). For instance this change adds ambiguity:

She decided to gradually get rid of the teddy bears she had collected.

To:

She decided gradually to get rid of the teddy bears she had collected.

A better rephrasing would be:

She decided to get rid of her teddy bear collection gradually.

She decided she would gradually get rid of the teddy bears she had collected.