Interesting Note and Reminder

As most anyone has probably noticed, this blog is pretty much inactive. However, I've looked back over it, and I wrote a lot of good stuff on financial mathematics, finance, and accounting. I'm still available for questions/comments at guardian.market@gmail.com. (I've set it to forward to my RL email, so I'll get emails much quicker now.)

Also, one item keeps surprising me. One post in particular keeps getting a lot of comments/questions. It's my one on how to make a stock index. Turns out, if you Google "How to make a stock index" it's result #4! I guess I'm one of the few that dared to delve into that topic.

I hope all is well in SL. I've pretty much left that world for real-life endeavors. Since I last posted, I've become an official actuary (title and everything) and that keeps me pretty busy. I'll try to post when I can. If anyone still reads this, post a comment to let me know!

Retained Earnings Part II

After I left the previous post, Bogart Beck, head of SL CapEx, and I had a nice discussion about RE, the Balance Sheet, and how things are supposed to be set up. Both approaches have their merits, but I wanted to explain his side of the story (as best I can), and show why the financial templates were set up as they were. (Note to Bo: If you were to post a current financial reporting template somewhere on CapEx, that would be much appreciated!)

In my previous post, I explained that

RE(t) = RE(t-1) + NI(t) - Div(t)

Which is still true, and it's how I learned it in my first accounting class. I believe this is also GAAP-compliant. Bogart, however, wanted to make it a little easier for the average investor to be able to "follow the money" through the financial statements from month to month, and in so doing, rather confused those who were more familiar with the previously stated method.

For SL CapEx, Bogart was trying to set up a system where the RE reported on the Income Statement was directly carried over to the Balance Sheet, and what was formerly in the place of the RE on the Balance Sheet was transferred to some other account, say Capital Surplus. So, at the end of the month, here's what the (simplified) journal would look like:

Account..................................DR....................CR

Retained Earnings................RE(t-1)...........................
Capital Surplus...............................................RE(t-1)

Net Income...........................NI(t)..................................
Dividends..............................Div(t)................................
Retained Earnings...................................RE(t) = NI(t) - Div(t)

This way, an investor can look and see how the Income Statement carries through to the Balance Sheet.

However, Bogart has confirmed (I believe) that the GAAP method is acceptable as well. At least, he hasn't stopped me from using it on SLR's finances, yet. I will continue using the GAAP method, as it is the one I understand best.

Retained Earnings

One little description, so much power. The description of Retained Earnings on the SL CapEx template balance sheet formerly read

"TAKE DIRECTLY FROM LINE 523 of INCOME STATEMENT"

And this description can still be found on a few of the financial statements running around CapEx. The unfortunate part about this description is that it is wrong. (For one, the income statement only goes to row 53 in Excel, so that should be a first clue that something is odd.)

Retained Earnings is an account in the Equities Section of the Balance Sheet. It is a cumulative (read that word again - cumulative) account of all earnings that a company has retained since inception - hence the name "retained earnings." The tricky part about this account is that it is cumulative. In order to calculate Retained Earnings (RE) correctly, you must do it from the start.

Let's think about how to calculate RE. The first question is, "What is earnings?" Most would agree that earnings can be calculated as Revenues - Expenses. The Income Statement labels that number as "Net Income," so we'll refer to earnings as Net Income (NI).

The next question is, "How does a company retain earnings?" It's actually easier to address how a company does not retain earnings, and that is by paying dividends. When a company pays a dividend, then it is distributing part of its earnings out to its shareholders, who receive them. Therefore, the part NOT paid in dividends is the part of earnings that is retained. We'll call dividends "Div."

So, then we have a formula:

Retained Earnings = Net Income - Dividends
RE = NI - Div

(The second equation is the same as the first, but in the shorthand I noted above.) This is the exact formula that is calculated on the Income Statement, Line 53 (in the template I'm using).

The problem is that this RE is not equal to the RE on the Balance Sheet. The RE on the income statement represents the CHANGE in RE for this period on the Balance Sheet. Here's an example:

April 2008: Retained Earnings is calculated to be L$1,200
May 2008:

• Company has NI = L$1,500 and pays Div = L$1,000
• RE on the Income Statement is calculated as NI - Div = L$1,500 - L$1,000 = L$500
• RE on the Balance Sheet is calculated as RE(old) + RE(new) = L$1,200 + L$500 = L$1,700.

We can also write out a formula for RE on the Balance Sheet. It goes:

RE(t) = RE(t-1) + NI(t) - Div(t)

In words: Retained Earnings this period equal Retained Earnings last period plus net income this period minus dividends this period.

I hope that clears up some of the mystery with this line on the Balance Sheet. I see a lot of companies with incorrectly calculated RE, and it's really a pretty simple line to do. If you have any questions, feel free to leave a comment - anyone can.

Where to Go?

Let's face it. Volumes on SL Capital Exchanges (all of them) are dismal, and liquidity is a major concern for investors. "Why should I plunk down several thousand of my hard-earn Linden Dollars if it'll take me months just to sell at a break-even price, and that's if I'm lucky?" With liquidity locked up, major investors will have a hard time realizing a profit on their investments, even if the market values of the particular stocks rise. So how do we fix this?

It seems that whenever a SL company goes belly-up, the CEO simply throws their hands in the air and walks away. That's because it's a possibility in Second Life. There is no chain connecting the CEO to the viewer which makes him or her responsible. Threats of legal action are simply idle talk, as even recovering something like $20,000 USD (about L$5.4 million) would be silly in the context of lawyers' and courts' fees (not to mention your time) to get it.

Certain exchanges have made progress in the realm of removing the complete anonymity of CEOs by requesting IDs for IPO clearance. Nevertheless, even if you know their ID, what good does it do you? Again, legal fees are too prohibitive.

I hesitate to say it, but I think it may be time to tie some more legal strings around the CEOs of SL companies. Some have suggested using promissory notes, but it sounds more like a fidelity bond issue to me, if there was an insurer who would ever cover it. The point remains the same, though: sending a message to CEOs that this is more than a game (in spite of the hypocritical boilerplate language at most exchanges), it is a responsibility which will reach out and slap you in real life if needed.

Before I let this tirade go too far, I do realize that this is not always something that a CEO wants to take on. I daresay that the salaries earned by most SL CEOs are nowhere near enough to compensate for the trouble which these legal ties could cause in real life. Maybe that's the answer, but I hope not.

I'd love to know how to restore investor confidence, but I'm just not seeing a way of doing it without giving investors some sort of recourse for CEO inadequacy or fraudulant activity.

Anyone else have other ideas? Comments?

It's been awhile...

So, it turns out I've been pretty bad at posting over the last few months. I've had things to keep me busy: one of my actuarial exams, work, RL moving, vacation, getting engaged, etc., so it's not like I'm short on excuses. Nevertheless, I think I should try to post and keep updating this thing periodically.

It seems like interest has waned in the market. I'm not entirely surprised, as most of the markets are rocked by scandal after scandal. New money coming in is kind of rare, as it seems that those who are involved with the markets currently are the only ones who would like to be involved. The lack of liquidity also frightens new investors, as the market value of securities is significantly more than the liquidation value (that is, if you sold all your shares as fast as you could) for almost every security, and even for modest amounts of shares.

For example, take SLR, the company I'm CFO for. (This is in no way a critique of my shareholders, but if I'm going to pick on a company, I might as well hit home.) Suppose I owned 10,000 shares of SLR right now. The market price shown on CapEx is L$6,500. However, if I actually tried to sell all 10,000 shares, I would receive (after commission) L$5,153.02, which is 79.3% of the displayed price. Make it 50,000 shares and I would only receive 12.9% of my displayed market value!!! And we're not talking vast sums of money here - 50,000 SLR shares at market is worth about $120 USD. Enough to care, but not enough to break most of us financially.

You can play this game with almost any stock on any market. There are exceptions, where management has taken care to set aside cash reserves to prevent this from happening, but by and large putting money into the market means you will need to take your time getting money out of the market.

I've heard the idea of market makers being tossed around before. For those of you who don't know, a market maker is a person/firm that makes money off the bid-ask spread in the market. They provide liquidity. However, from my previous actuarial exam (which I passed, by the way!), Modeling Financial Economics, market makers need options in order to protect themselves. There are techniques whereby market makers can insure themselves against large price changes, or even set themselves up to make money if the market doesn't move. However, these require options, which no exchange in SL has been willing to set up yet.

If any exchange in SL is seriously interested in setting up options and market making and similar techniques, please contact me. While I'm sure I'm not the only person in SL who understands how to make it work, I'm likely one of the few, and I would love to help.

I suppose the question is this: How do we revitalize the markets now? I think liquidity is the major issue, but I would like to hear what others think as well.

Benevolent dictatorship

Noun: A dictatorship in which the leader has power only because the people choose to allow them to remain. This necessitates a wise use of power and generally prevents abuses since the benevolent dictator loses power if they are unsuitable. (From the Wiktionary)

Why this post? There is currently some debate going on here at Your2ndPlace and at the International Stock Exchange.

The debate seems to be "Bottom-Top Vs. Top-Bottom" management/regulation and according to someone the VSTEX has moved from the first to the second stance, effectively aligning with the WSE.

This post will be probably disappoint someone. It won't be a deep analysis of the pros and cons of both stances. Here I won't be trying to change anyone's mind. People have been arguing on issues since the human race was born. They'll still do after this post of mine.

First off, to me financial markets on Second Life could be related to the situation in the US before the Securities Act of 1933. You can translate that into "an unregulated situation" if you like. Since that Act, more steps were taken but we won't go over the whole process now.

Let's just say that in SL we lack a lot of things (when it comes to policies, regulations, governing bodies and applicable laws) that we can have in "real life".

When the VSTEX was started there was an optimistic view of a community wanting and willing to work together, in order to build a lively virtual stock exchange. That was the philosophy before I joined the VSTEX (which happened a few later of it going public) and I must admit I quite liked it.

It did not work that way though. Now one may say that we just changed our mind, that we woke up one day saying "To the hell with shareholders, we'll do what we want and so be it".

Over the time we found out (the hard way) that exchange users were of 2 kinds: educated and uneducated (with the latter group being apparently the majority). Educated users know what they do, they often know how to game the system, sometimes they are not so well intentioned and they may resort to practices that would be frowned upon in the real world (when those practices are not outright illegal).

Of course there is nothing wrong with educated users per se, on our exchange there is plenty of well intentioned, honest, educated users.

Maybe we failed to create the conditions to develop a thriving community capable of setting standards and rules. That's a possibility. At the beginning we were too new to have a significant amount of honest, well educated users. There were the WSE, the SLCAPEX, the ISE. Extablished, bigger markets.

It didn't take much time before we had to face the Jasper Tizzy issue. Everyone who's been following SL financial news for a while should know about it. That led us to the conclusion that extra steps had to be taken, steps that the community wasn't still asking for. Almost all the requests we got at that time were along the lines of "Where's my money, I want my money, give me back my money".

Following that, we had to take a decision (someone here may argue "You really had to?" to which I would answer "Hell, yes") because we really did not like the "The CEO has fled, there's no money left, the company is delisted. Have a nice day." attitude that was standard for other exchanges I believe, before WSE's WTF (World Traders Fund) was born.

That decision was, to look for someone willing to take over the company (actually, the name and the listing with us since no money was left behind by the old CEO), trying to revive it and turn disgruntled shareholders into happy ones. At that time we did not realize it, but it was the first step for top-bottom management and regulation. Nobody ever asked for that (maybe because it was so unusual?), yet we did it. In the aftermath of the AVC history, I can tell we opened a canning of worms. However, I don't regret that decision. None of us VSTEX managers does.

Since then there have been issues with other companies and while the rules we've been adding have been implemented without directly asking the investors or running polls, the investors (of course, some of them) themselves have been asking us via emails and support tickets to build up our rules and make our control on listed companies more tight.

I'll quote Konner McDonnell:

"Evolving. Changing. Remembering. Like I expect all virtual exchanges SHOULD."

And Cocky Dagger:

"Sometimes issues can be more complicated than they appear and I would say the obvious choice is not always the best choice. I actually started out early on with one belief and time and experience has caused me to do a 180 from where I was at."

We reckon that some sections of our website should be updated and that we may want to rethink our strategies and goals. I could go on for miles here, however I'll cut it short here. I'll just invite everyone to our General Discussion forum (a VSTEX account is needed to login update: now everyone can browse our forums). We're always open to discussion.

Options: Lesson 2

Guardian's Note: This is a continuation (though much overdue) of a previous post which I wrote awhile ago. Reading that post will likely be necessary for a good understanding of this one.

Now that you have a good intuitive understanding of what a call and put option on a stock are, and how to use them, let's think about how to price them.

When building a model for options pricing, there tend to be a set of convenient assumptions made to simplify the process. First, there are no transaction costs or taxes. Secondly, you can buy or sell as much of any stock/option without altering the price. Thirdly, volatility (we'll get to that later) will be known and constant. I think that's all I'll need for this lesson.

Certainly, the value of the option is determined by the value of the stock at some given point in time. If the option is European, then the only relevant value is the price at the end of the time period.

Suppose we have a stock at price S₀ currently, and there is a European call option expiring at time 1 with strike price K = S₀. Now, in this particular oversimplified world, the stock can only take on two values at time 1: S_u and S_d, standing for an "up" movement and a "down" movement. Since the option is at strike K = S₀, the option will pay (S_{u -} S₀₎ at S_u and zero at S_d. We'll denote these values by C_u and C_d respectively (representing the value of the call at an up movement and the value of the call at a down movement).

The price of the option can then be calculated as

C_u * P(up movement) * v

Where v is the present value factor to discount the payoff with interest back to time zero. We'll need an interest rate to do that, which we'll call r. We'll also need P(up movement) (the probability of an up movement) to calculate the price.

Through some mathemagic which I think I'll gloss over for now (but if you all want to see it, I'll happily spell it out), a probability which correctly calculates the price can be found using this formula:

P(up movement) = (e^(r-d)*h-d)/(u-d)

Where r is the continuously compounded rate of return, d is the continuously compounded rate of dividend payments, h is the time period (in years), d is the multiplicative factor by which S can decrease over h, and u is the multiplicative factor by which S can increase over h.

There are also formulas for u and d, but if you need those I suggest reading this.

With all of that in place, there is now a formula for pricing a call option where the stock has only two movements, up or down. This model can be expanded to include more periods, use discrete dividends (say the stock pays $10 at time 0.75), handle American options, and do a variety of other nice tricks. However, the more important fact is that this is the backbone of the famed Black and Scholes model, which I will discuss in Lesson 3.


I hope you can see how this all gets very hairy mathematically very quickly. Some of the background I jumped over is done not by mathematical proof, but by economic logic, which may not sit well with some mathematicians. I have also tried to simplify a lot of this to be read by the general audience, whereas for the last four months I've been studying the specifics of this, and more complex models, extensively. If any of you readers are curious about this topic on a deeper level, feel free to post here, IM me in world, or email me at guardian.market@gmail.com. I can't guarantee I'll know the answer (it's a big world out there with options!) but I'll try to at least point you in the right direction.

My Lack of Posting

...has been due to studying for my next actuarial exam, Exam MFE (scroll down a little to the Financial Economics segment).

I'll be more active after the 15th.

My apologies for the lack of mathematical reading.

Mathematical Evangalism: The Monty Hall Problem

Every once in awhile, I have to go on a streak of public education for the betterment of society. The Monty Hall problem presents such an opportunity and just cause for such evangelism, as this non-intuitive probability problem routinely trips up even sharp-minded folk. So, I present to you a problem:

Suppose you're on a game show. You've made it to the final round, and there are three doors presented. Two of the doors have a goat behind them, meaning you win nothing, and the third holds a new car. Choose the door with the car, and you win that. You make your choice, and before revealing your choice, your host (Monty Hall, hence the name) opens one of the remaining two doors to reveal a goat. He then asks you if you'd like to switch. Is it advantageous to switch doors? What is your probability of winning if you do/do not switch?

...think about it...

...got an answer in mind yet?

The surprising answer is that switching gives you a 2/3 chance of winning. Most people guess 1/2 - there are two doors remaining, and one of them is right. However, let's think of this differently.

When you first choose, you have a 1/3 chance of getting the right door. Then, an incorrect door is revealed. If you were originally right and you switch, you're now wrong. But if you were originally wrong and you now switch, you're right. Because you had an initial chance of 2/3 of being wrong, by switching you now have a 2/3 chance of being right, hence the answer.

Don't believe me? Play a few rounds online and convince yourself.

Land Prices

Linden Labs announced recently that it would be dropping prices of land sales significantly. New islands, for example, will only cost USD$1,000, down from USD$1,675 as last I recall.

Talk about a way to piss off your most loyal supporters! Everyone currently holding land just took a major hit to their resale value, and my understanding was that land prices had been dropping anyway. While this will certainly encourage new growth, I think there will be a painful period of losses for existing (especially startup) businesses as well. As the new land is sold, those owners can price their rents lower and simply outbid the current ones still paying off their $1,675.

Linden Labs is obviously placing a bet on the elasticity of demand for land. Elasticity, for the uninitiated, is how much the quantity demanded of a good changes with respect to a price change. Some goods, like (some) electronics, are very elastic - small drops in price will produce large sales and vice versa. Other goods, like salt, aren't elastic at all ("inelastic") - you can double the price of salt, and people will still buy about as much as they did before. A few very rare goods, like gasoline, are inelastic in the short run and elastic in the long run...but I'm getting off-topic...

If the demand for new land is elastic, LL will see a large jump in sales for their drop in price. My guess is they're hoping this outweights (a) the amount of anger they're generating, and (b) the amount of extremists who go researching into OpenSim projects.

Let's see how the bet pays off.