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  1. #1

    Implementing High Finance in WoW, part 2: Inflation and Discounted Cash Flow

    This was originally posted in the Wind Trader's Stormspire on 28th "November 2010. Moving it into the public forums for greater benefit and just an interesting/insightful read. - Sinshroud.

    Inflation exists in wow. That is, the value of gold changes over time and it generally decreases in value. This (short) post is an attempt to quantify inflation and to use it to explain how a concept called Net Present Value (NPV) works in finance.

    NPV is a core financial descision-making tool. If you do an NPV calculation, and it's positive, you should (with a lot of caveats I'll explain later) make the trade. This is a tool that is directly transferable outside of warcraft - most financial decisions that you make will benefit from a back of the envelope NPV calculation.

    Here is a really simple example of an NPV calculation:

    Suppose I see a Hyacynth McCaw sitting on the AH for 9000g. Now, ignoring all transaction fees (AH cut, relisting, etc.) I "know" that it's worth 15,000g on my server. Should I buy it and relist it?

    All NPV does is make the decision making process a little more obvious. It does this by looking at the cash flows for the lifetime of the trade. Thus:

    Day 0: -9000g
    Day that it sells: +15,000g
    Expected Value (EV): +6000g

    So far, so good - it looks like this trade will net us 6000g. Still, that "Day that it sells" is very vague. Let's try to quantify that a bit more. Let's say we know it will sell in exactly 30 days, and we know this with 100% certainty.

    It's still +6000g, but how much is that REALLY worth, given that we are going to tie up our cash for 30 days? To calculate this, we need to have a value for inflation.

    To get this value, I looked at the priceof a commonly traded item that started out very high when it was first available and slowly dropped to almost nothing: primordial saronite.



    See the smooth descent from 600g to 100g in 3 months? That's a drop of around 83% in 3 months, or about 27.7% a month. I'm going to use this number as a first stab at an inflation figure.

    Just a reminder of what this means: we would be equally happy with 100g now, or 127.7g in 30 days. An investment that cost us 100g today and paid off 110g in 30 days would not be good for us. This may not be right, but we are at least in the right ballpark - with more analysis (a "basket of goods") we could do better.

    Back to the deal:

    NPV = -9,000 + (1 - 0.277)*15,000 = 9000 - 10845 = +1,845g

    It's positive, so the deal is still a good one, but it's not nearly as good as it looks when you see that +6000g figure. Now, let's add some risk.

    I'm going to assume for a moment that I know the market for Hyacinth McCaws on my server. On average, on any given day, there is a 5% chance that my pet will sell. What does this mean in real life?

    Remember that the 5% chance is independent - if I went 100 days without selling the pet, it's still just a 5% chance of it selling the next day. therefore:

    Chance of sale on day:

    1: 5%
    2: 9.75%
    3: 14.27%
    ...
    30: 78.6%

    Let's say that after a month, if it doesn't sell, I'm going to sell it for half price (7500g) to get a guaranteed sale that day. Let's also say that even if it sells on day 1, I am not going to use the money until day 30 (this is to simplify, for right now).

    (0.786*15,000) + ((1-0.786)*7500) = 11790 + 1605 = 13,395g

    Pretty good!

    But now we need to take into account inflation:

    NPV = -9000 + (1-0.277)*13395 = 684.585g

    It's still positive, so it looks like it's going to be a good deal, but now we really have a solid idea of how good a deal it is. If the 9000g represents most of our assets, we now have the ability to decide if this is the best use of our money, or if there is another, higher NPV, deal that we would be better spending our money on.

    Perhaps the 9000g could be spent on something that will sell for 11,000g but it's guaranteed in a week:

    NPV = -9000 + (1-((0.277/30)*7))*11000 = -9000 + 0.9354*11000 = +1289.4

    The second deal, despite giving us less cash, has a higher NPV and we should take that deal instead.



    So, what was the point of all this?

    The point was to explain how to make good descisions in the face of risk and inflation. There is a lot more to take into account, and I fudged the numbers a bit (I should have had 30 different calculations for the McCaw, not just 1) but hopefully you can at least understand where I am coming from.

    If anyone is interested, I'd be happy to share some spreadsheets where you can input the deal you are considering, the chance of it selling in a given day, the "salvage value" and your own best guess at an inflation number. I'd also be interested in modifying the inflation number to dynamically update based on data on a basket of goods from the undermine journal for your particular server, but perhaps that is for another day.
    Last edited by Sinshroud; July 12th, 2011 at 07:07 AM.

  2. #2
    Thanks for this Deathspiral. I was looking for a proper understanding of the maths behind all this, and you made it really simple for me. I've been looking to use data from MarketWatcher for a few common items come Cataclysm. The only problem with the addon is that you have to add items to watch, and you have to remember to ask it to scan for you. Having access to TUJ's data would be much more interesting.

    I'd also be interested in modifying the inflation number to dynamically update based on data on a basket of goods from the undermine journal for your particular server, but perhaps that is for another day.
    This and the spreadsheet interest me, because I like maths (just out of practise right now). I'm curious about whether you can do this already, or you're talking about needing raw data from TUJ.
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  3. #3
    Thorzek's Avatar
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    First of all, why would you pick Primordial Saronite to measure inflation? That's not at all representative of market forces. That started out with a massive supply/demand imbalance that changed drastically over time. To measure whether or not an economy is inflating you want to sample general categories of equal relative worth - a tradeskill powerleveling kit would be an excellent example.

    Second of all, the decline in price an item has over time isn't inflation - it's deflation. Inflation is the rise in the general level of prices of goods. If I have a million gold today and can buy 100 primordial saronites, but in 3 months I can buy 127.7 my purchasing power went UP, not down.

    I'm going to stop here because I don't want this to seem like an attack. You've got a good topic here but you're not displaying it properly.

  4. #4
    Agreed, it's wrong. I should have used "appropriate discount rate" instead of inflation. I'm so used to working with standard (inflationary) markets that the two terms had become close to synonyms when trying to explain things to people. I actually started to edit my post right after posting to make this clearer and then decided that no one would care. I was wrong

    Usually, when trying to work out what a good discount rate would be, you could look at the risk free rate and then take a stab at how risky the investment was in order to get a good idea of the discount rate to use. Sadly, WoW lacks t-bills or a good similar proxy and, indeed, doesn't have banking systems at all. Because of this, many basic economic models don't work.

    The reason I use Primordial Saronite to calculate the discount rate is that it's a good proxy for how the value of gold changes over time. Here is my thinking: WoW is a world of infinite resources - the only thing that matters is time. As time progresses, the majority of resources that are commonly consumed by players become less and less scarce (and less and less valuable).

    Almost every good in wow is deflationary because supply increases and demand decreases as time passes - in this respect it's very similar to the technology industry. In tech, the whole Consumer Price Index (CPI) idea of taking a basket of goods and tracking changes doesn't work very well simply because the basket of goods changes so quickly as to make comparison very difficult. e.g. it's hard to measure how the price of 5.25" floppy disks has changed in the last 20 years because these items are almost never sold any more.

    If most goods deflate from the beginning of the release of new content (peak) to the end of new content, the the market _as a whole_ is deflationary. In a deflationary market, well, stuff breaks. Lots of assumptions built into economic models break down and you have to start talking about deflationary spirals, Giffen goods and all kinds of other theoretical stuff that, frankly, I don't have a good enough grounding in to discuss.

    So, instead, I decided to use a simple thought experiment: If I was a consumer and I wanted to buy Primordial Saronite (or any other base good - raw gems, raw enchanting mats, etc.) at the beginning of the expansion, how much would someone have to pay me for me to wait a month and buy it then? This seems like a good proxy for the discount rate.

    If using Primordial Saronite bothers you, you can use a basket of goods like all gems and enchanting materials - they almost all fall in price from the point of release to the point of the next round of content coming out.

    Anyway, point well taken - "discount rate" is a much better term than "inflation" and I should have made the correction when it first occurred to me.
    Last edited by Deathspiral; November 29th, 2010 at 06:40 PM. Reason: clarification about the "majority of resources"

  5. #5
    Oh, quick point about the tradeskill kit: that idea only works if the "tradeskill kit" basket is a good measure of goods that are commonly bought by the average consumer and therefore representative of the total market. I'd strongly argue that this is wrong - old mats do NOT properly represent what the average consume buys on an average day. To use a tradeskill kit or something else based on "old" mats would be like measuring inflation solely by watching the prices of replacement parts for a 1970's mustang.

    Perhaps the best measure of inflation lies not in goods at all, but in services: how much is the average repair cost for a full repair changing over time?

  6. #6
    If I remember correctly, repair values are based on the vendor value of an item (or what the vendor value would be if it had one). With that in mind, you could potentially use the vendor values of items.

  7. #7
    Namssob's Avatar
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    Quote Originally Posted by Deathspiral View Post
    Oh, quick point about the tradeskill kit: that idea only works if the "tradeskill kit" basket is a good measure of goods that are commonly bought by the average consumer and therefore representative of the total market. I'd strongly argue that this is wrong - old mats do NOT properly represent what the average consume buys on an average day. To use a tradeskill kit or something else based on "old" mats would be like measuring inflation solely by watching the prices of replacement parts for a 1970's mustang.

    Perhaps the best measure of inflation lies not in goods at all, but in services: how much is the average repair cost for a full repair changing over time?
    Actually, I disagree with your 1970's Mustang analogy. A tradeskill kit is more like "car", vs. something as specific as 1970's Mustang. I could see the example working if there were 20 different JC "specialties", and every patch, a new set of 10 more specialties were introduced, some just "newer" versions of an older specialty. In that case, yes, the Patch 1.3.4 JC Specialty kit mats would not be a good measure, much like the 1970 Mustang would not be. But in the real world, if there was only "CAR", then yes, the spare parts for "CAR" would be the same as the mats for JC kit.

    But otherwise, this thread is awesome - thanks!
    How To: Create And Sell Profession Kits ---- MoP Shuffle Flowchart ---- Article: A Case For Dual Gathering
    "Never underestimate the sheer amount of derp the majority of WOW's playerbase possesses." -- Belrandir
    "They could have offered me free ERPing in Goldshire with real women over Skype for the next year and I would have passed." -- Zerohour
    "Scissors are OP. Rock is fine." --Paper

  8. #8
    This whole thread is actually very interesting from a real world economic perspective. When people say "inflation" they are usually talking about the CPI-E or another variant. The problem is, every measure of inflation uses a different basket of goods and each basket changes over time.

    Is a "mid sized family sedan" (to paraphrase one item from the CPI) from 1970 even remotely comparable to one from 2010? The one from 2010 may not even run on gasoline and certainly is filled with lots of technology that the 1970 car would not have. Indeed, it's very, very hard to get this right, which is why many people are deeply suspicious of the governments CPI figures in general.

    For example, they changed the definition substantially about 12 years ago and, just like that, inflation went from pretty high to completely manageable, not because anything actually changed, but just because they decided to engage in a spot of accounting trickery. (see shadowstats.net)

    Anyway, back to wow:

    Something that I forgot to mention about NPV is that it works over many time periods. For example, lets say you are trying to decide if you should buy not one, but three mccaws from the AH, all sitting there at 9000g. Lets say you know you will sell one every 30 days to keep things simple and lets say all the numbers above haven't changed. Now, is buying all three of them a good idea, knowing that you'll only be able to sell the third in month 3? Let's take a look:

    NPV = -9000*3 + (1 - 0.277)*15,000 + (1 - 0.277)^2 *15,000 + (1 - 0.277)^3 *15,000

    = -2,645g

    So, assuming you accept my discount rate of 27.7% (a big if, but one we can work on over time), you should NOT accept this deal.

  9. #9
    The problems of cutting an pasting are that if you made a typo once, you make it everywhere...

    we should be using (1/1+rate) NOT (1-rate)!

    I'll fix later, I'm stuck in a conference call right now.

  10. #10
    Thorzek's Avatar
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    This whole thread is actually very interesting from a real world economic perspective. When people say "inflation" they are usually talking about the CPI-E or another variant. The problem is, every measure of inflation uses a different basket of goods and each basket changes over time.
    I think you mean CPI-U. -E is an experimental index for the Elderly from the mid-90's.

    In tech, the whole Consumer Price Index (CPI) idea of taking a basket of goods and tracking changes doesn't work very well simply because the basket of goods changes so quickly as to make comparison very difficult. e.g. it's hard to measure how the price of 5.25" floppy disks has changed in the last 20 years because these items are almost never sold any more.
    That's why a good CPI doesn't measure changes in specific goods, but rather market bundles. It's not representative to measure 5.25 floppies, but it is representative to measure "average sized storage media" which 15 years ago was one 5.25 floppy but now might be a 20GB flash drive. In the US the BLS reports very, very general categories for this reason.

    http://www.bls.gov/news.release/cpi.t01.htm

    Is a "mid sized family sedan" (to paraphrase one item from the CPI) from 1970 even remotely comparable to one from 2010?
    It absolutely is.
    The one from 2010 may not even run on gasoline and certainly is filled with lots of technology that the 1970 car would not have.
    Which are irrelvant at the macro level. CPI isn't supposed to measure against significant changes in standard of living. You measure a 1970 car against a 2010 car with similar options. If power windows cost more, you don't measure using them. You don't measure a Honda Civic from 1970 against a 2010 Honda Civic because they are no longer representative of what they were in 1970 - a more accurate comparison would be an entry-level hatchback car - I have no idea what model this might be because I don't shop for cars - a Mitsubishi Mirage? Hyundai something?

    For example, they changed the definition substantially about 12 years ago
    Not sure what specifically you are referencing here - the BLS made significants adjustments based on the results of the Boskin Commission which showed that inflation was being overestimated.
    and, just like that, inflation went from pretty high to completely manageable,
    Most of this was the result of CPI remodeling to accommodate significant changes in medical spending and reporting. Simply put, prior methods were overestimating costs because improvements in treatments and efficiencies were being realized in the real world but not modeled properly by BLS.
    not because anything actually changed, but just because they decided to engage in a spot of accounting trickery. (see shadowstats.net)
    I don't buy anything John Williams says. His methodology is, at a very minimum, just as flawed as the system he purports to "correct". Hogwash.

 

 

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