Simple Pound

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People, it gets more and more depressing to write these end of the month reviews. Net worth down 5% this month. That’s huge. I think I have abandoned the whole “delayed gratification effort” for, well, instant consumption. On the other hand, I have taken up an old hobby again that I haven’t had time for since I first went to University - horse riding. As you can imagine, it’s eating up my cash faster than I can earn it. But you know what? I’m not going to apologise. I’m having fun, I’m enjoying myself and I was so happy while cantering through the countryside - I decided it was worthwhile.

Nevertheless I have been spending a bit carelessly recently (birthday week, what can a girl do?) and much of that cash went to unnecessary expenses like drinks, nights out, cabs home - you get the picture. Oh and there’s shoes. Gorgeous shoes. I blame Karen Millen

This is probably the point where I should say “It’s all going to change”. Well, I’ve tried that before and I’m not convinced it’s worked yet. I’m on it, wish me luck.

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Thanks to Rob @ Money Watch I didn’t miss this comprehensive overview of the credit crunch by the BBC. It is essentially a collection of key graphs to represent the economic changes in the last 12 months and I wanted to cherry-pick my favourites to share with you - but not necessarily because I agree with the message they are intending to bring across (hence the question mark in the title…)

Let’s start with a picture highlighting the key changes in our economy since the start of the credit crunch. The message is clear - petrol and food, two essential cost factors in nearly every household, have increased significantly in price over the last twelve months while the value of our homes has been eroded by approximately 4.4%.

With the rise in petrol prices come further cost increases in related fields such as energy or holidays (think airfares…). But did anyone ever stop to think that this has actually nothing to do with the credit crunch per se? Through an unfortunate coincidence we see a boom in commodities prices at the same time as our economy is already suffering from the aftermath of the subprime crisis - yet that doesn’t mean one caused the other.

Similarly, the food inflation we witnessed in the last couple of months originated in the commodities boom that saw prices in wheat and other agricultural produce reach heights of unprecedented nature. I agree that it has been rather extreme and that certain products seem to have been increasing at the rate of a penny a day, nevertheless that doesn’t automatically mean it’s a direct cause of the credit crisis.

More importantly I’m starting to wonder whether conditions like this couldn’t have been avoided if only people/businesses would have appropriately used hedging. Only today I read that South West Airlines still bought its fuel for $26 a barrel at a time when the market price had reached $80 (slightly old example, but it illustrates my point). How come the likes of Tesco’s, Sainsbury’s or Marks & Spencer’s didn’t come up with a clever idea like that? After all, hedging was introduced for companies to sell their risk in exchange for a small premium and stable input prices.

Before I rant even further, let’s move on to the last category in the summary picture: housing. If you have been reading this blog for longer than just a few days, you will know that I join forces with all the other people struggling to get their foot on the housing ladder and hence eagerly awaiting a double-digit drop in house prices. I totally emphasise with anyone who is worried about negative equity but if you are living in your house because it is your home then you have almost no reason to be overly worried. Hopefully nobody will be forcing you to sell any time soon, hence you can simply wait it out and I’m certain that we will see prices returning to their historic levels (with the only difference that hopefully a few more first-time buyers will have joined the ranks of home owners). And even if you are looking to sell and for whatever reason you cannot wait a few more months or a year until you do so, there are a one-hundred and one things you can do to enhance the value of your home.

In any case, my actual point was related to the graph below. After you got over the fact that house prices have officially been falling since April, have a closer look at the second graph with details of house prices over the last 10 years. Note that it charts the annual change in house prices - that means, as long as the graph runs above the 0 line, your home will have increased in value. Looking at your portfolio or pension account - how many investments can you quote that haven’t fallen in value once over the last 10 years? I doubt there will be many.

What I’m trying to say is that a house purchase has always been a good and solid investment with annual returns of anywhere up to nearly 30%. Now, for the first time in over 10 years we’ve seen a careful reversal of this trend and the world is in panic. As I said before, I totally emphasise with people worried about negative equity, especially as a house purchase is such a major investment, maybe the biggest one many of us will make in our life. However, that put aside, any investment bears the risk of losing as well as gaining in value. Why should property be different?

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When I started to research the risk element of my Portfolio Returns series I had no idea what can of worms I was about to open… from the lack of consensus regarding what risk actually is and how it can be properly defined and measured to an abundance of metrics trying exactly that. The different approaches vary significantly but most of them have one thing in common - a high level of abstraction and greek symbols

Don’t get me wrong - I find this extremely exciting and interesting and I’m certainly going to write about it in the near future, but from a logical point of view it might make more sense to cover a few statistical concepts first.

This is why I will be changing the initial order of the Portfolio Returns series to the following:

1. Post : The Basics  (covered on June 28th)
Arithmetic mean (average loss, average gain), geometric mean, frequency distribution, maximum value, minimum value, positive # of years / months / weeks, negative # of years / months / weeks.

2. Post : Statistics (previously 3rd post)
Standard deviation, semi-variance (semi-deviation), downside variance and below-target probability.

3. Post : All About Interaction (previously 4th post)
Covariance: degree of variability of returns between two assets, correlation coefficient, units of annual return per unit of standard deviation, expected final value of $1.00 / £1.00.

4. Post : First lesson in Greek (previously 5th post)
Beta coefficient or an assets’ degree of responsiveness to market movements.

5. Post : Advanced Greek (previously 6th post)
Alpha or superior returns.

6. Post : More Jargon (previously 7th post)
Sharpe ratio.

7. Post : Risk (previously 2nd post)
VAR: value at risk, M-squared.

I think this order will prepare us nicely for the last topic which also turns out to be the most challenging and complex. The post on Statistics will follow shortly, stay tuned!

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This won’t quite be a conventional Personal Finance post, but the fact that I cannot calculate my portfolio’s performance without converting negative returns into “false positive” ones annoyed me too much to just ignore. Since I couldn’t find a straightforward way around it, I decided to simply code the Excel function I was looking for myself.

While the code is by no means perfect (yet) it does the job nicely and I’m nevertheless pleased with the result. As long as it gets called properly, it converts your negative percentages into a value equivalent to (100 - x) / 100 where x is your percentage. For positive values, it does the conversion according to (100 + x) / 100. These conversions means that a decrease of 10% will be expressed as 0.9 and an increase of 10% as 1.1 which subsequently allows you to compute the geometric mean (which is exactly what it does).

Below is the VBA code you will need to utilise this functionality. Feel free to use it as you please but don’t worry if you have no clue how exactly to do that. I have included a step-by-step description of how to install and call it from your Excel worksheet underneath the code.

Function geometric(data As Variant)
     Dim vaData As Variant
     Dim rnData As Range
     Dim i As Long
     Dim j As Long
     Dim iblank As Long
     Dim jblank As Long
     Dim bblank As Boolean
     Set rnData = data
     vaData = rnData.Value
     temp = 1
     n = 0
     For j = 1 To UBound(vaData, 2)
          For i = 1 To UBound(vaData, 1)
               If vaData(i, j) <> Empty Then
                    vaData(i, j) = 1 + vaData(i, j)
                    ’ compute product for non-empty data cells
                    temp = temp * vaData(i, j)
                    ’ count number of items in list
                    n = n + 1
               End If
          Next i
     Next j
geometric = (temp ^ (1 / n)) - 1
End Function

Follow the steps below to make the above function available in your Excel worksheet:

1. In Excel, open the file you want to use the function in. Note: at the moment the function will only be available on a per-file basis. That means, if you’re planning to use it in more than one file, you will need to repeat this procedure for every single file. I’m working on coding a proper add-on that you simply install into Excel and hence make available to any new or existing file. I told you it was work in progress…
2. In the menu bar, next to the entry “File”, right-click on the Excel icon and select “View Code”
3. The Microsoft Visual Basic Editor opens and you stare at a blank document
4. In the menu bar, click on “Insert” followed by “Module”
5. Copy and paste the above code into that “new” blank space and hit “Save”
6. After you have saved the changes, click on “File” and select the entry “Close and return to Microsoft Excel”. This brings you back to where you started, and your function is ready to use.

Here is how you use the function:

1. Open the file in which you have installed the above function
2. Pick a cell that you want the result to contain and type “=geometric(”
3. Note the opening bracket !
4. With your mouse click and hold until you have highlighted the cell range that contains the numbers you want the geometric mean of. Alternatively, type the cell range yourself as A1:D4 where A1 should be replaced by the coordinates of your first cell and D4 should be replaced by the last cell’s identifier. At the moment, the geometric function only works with a cell range, not individual cells or numbers. I’m working on it…
5. Close the bracket by typing “)”
6. Hit ENTER to see the geometric mean of your highlighted cells

If you format the cell in question in such a way to convert your result back into a percentage (just right-click, choose Format - Number Format - Percentage), the result should make sense in the context of portfolio returns.

Note that the code above has been tested and verified in Excel 2002 and should work with any other Excel version(s) since. The only concern I have regards the compatibility with - you might guess it - Excel 2007. If anyone manages to run it under the new Office version, please let me know!

As usual, if you have questions or concerns, find a bug or just need a hand to get it to work, just give me a shout or leave a comment! I hope you will find it as useful as I did.

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One thing is for sure - reviewing last month’s financial odyssey is not going to be fun. On the other hand, I suppose I should be thankful for keeping such a close eye on my money since otherwise I would have never noticed the appalling truth. Or learnt from it. My point is:

I am now worse off than three months ago.

Despite three months’ salary and pension contributions my net worth is below the March level. I’m absolutely shocked and even a little unhappy since I enjoy seeing the progress bar increase (as opposed to decrease by nearly 2% this month)!

At least I have a pretty good idea what led to this fiasco: an orange coat, a digital piano and a trip to the Caribbean. In hindsight, would I commit these “sins” again? Maybe, yes and yes. The coat, I fully admit, was an impulse buy and a very expensive one at that. Yes I needed a coat, but no it didn’t have to be that one. On the other hand, I still love it as much as I did the minute I walked out of the shop with it and have so far not seen a single person (other than me) wearing it. In a city like London that’s pretty impressive

My piano purchase was an even larger expense than the coat and by no means an impulse buy. In fact, since leaving home I had told my parents I would take my piano with me as soon as I had finished University and had a permanent place to live. Unfortunately it turned out to be prohibitively expensive to ship an item like a piano from Germany to the UK. Hence I decided to get a digital piano in the meantime so that I could start playing (and practising!) again after having not touched a single key during my undergrad studies. The model I ended up getting was only half as much as the Yamaha Clavinova I had set my heart on previously and I got it for £100 less during an end-of-season sale. Regrets? None.

And finally, my holidays. One week on Grenada, a tiny little Caribbean island just north of Trinidad and Tobago. Flights and hotel together came to just over £400 and despite regular dinners out, numerous activities on the island and a day at a local spa, the holiday was definitely on the cheap side. Considering it was the Caribbean anyway Again, I don’t regret this trip at all. On the contrary, I would have happily stayed and travelled much further and for much longer than I was able to. The numerous once-in-a-lifetime memories made it worth every penny.

Regardless of whether I consider this money well spent, it’s time to stop. I am basically exactly where I was three months ago, so for the next quarter I will need to curb my spending in order to get my growth and progress back on track. Given that the house market is still in a pretty bad place, I probably won’t need my deposit money for at least another six months. But by then I definitely will need to have accumulated enough to make this (temporary!) backdrop in net worth unnoticeable.

If you have kept a close eye on my progress page you will notice that I redistributed some of my money between the various goals. I depleted my emergency fund in favour of allocating more money to the house deposit and I also shifted more money into the account intended to cover the outstanding bill I have with my parents. The latter is now fully funded, while my deposit has grown to 70% of my initial goal of £20,000.

Given that we’re halfway through the year, it’s once again time to have a look at how well my budget is working out. The good news is that my interest income reached 73% of my goal for 2008 by the end of June, indicating that my savings are working hard for me while I sleep This is even better news when you consider that this goal was revised upwards twice already this year: from £200 to £300 to its current value of £600. I decided to change it once more to £750, which is definitely fairly ambitious given that I received the interest from a fixed one-year term monthly saver account when it matured in June (hence half of that interest was technically already earned last year).

In the interest of brevity, I will only list the remaining changes to the budget (since I don’t deem them noteworthy enough to dedicate an entire paragraph to each):

• Utilities: new category with £350 since it took our utility provider more than 7 months to get our bill sorted and we hadn’t paid anything until they finally managed to get organised
• Landline: slightly up from £90 to £100 based on usage
• Mobile: down from £220 to £180 based on usage
• Groceries: slightly up from £1,400 to £1,500 - inflation is kicking in
• Dining out: down from £1,000 to £900 to accommodate the increase in food prices
• Clothes: up from £1,000 to £1,200 with the best intentions to undercut it
• Gifts: up from £750 to £1,000 (I’m too generous for my own good)
• Hairdresser / Manicure: up from £500 to £600
• Drinks: pooled with the Category “Clubbing” hence total down from £250 to £200
• Cinema: up from £50 to £100
• Health Insurance supplement: up from £60 to £65 - I blame the bad £/€ exchange rate
• Gym: Down from £360 to £150 because I cancelled my membership
• Contact lenses: Up from £200 to £500 as an eye infection forced me to change my prescription to the more expensive daily disposable lenses
• Life Insurance: Up from £900 to £950 due to £/€ exchange rate
• Broadband: Down from £100 to £90 as we are on a fixed subscription
• Charity: Up from £120 to £150
• Planes: Down from £900 to £800 as my one major holiday is already accounted for
• Holiday Accommodation: Up from £300 to £500 due to major naivety on my part (initially)

That’s all from me for now. Progress page and “Best Of” section have been updated as usual.

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I’m back from holiday and it’s time to start my new series on portfolio returns (as discussed in my previous post) with some basics on averages, limits and other interesting information you can extract from your data without too much effort. Since I’m working on a spreadsheet alongside these posts, I will also include some Excel references that you can use to shortcut the calculations.

Based on my outline, this is what I’m looking to cover in this post:

• arithmetic mean
• geometric mean
• frequency distribution / histograms
• maximum and minimum value
• positive / negative number of weeks / months / years

Arithmetic Mean

The arithmetic mean is more commonly referred to as the average (or just mean) and is calculated by summing all numbers of a list and subsequently dividing the result by the number of items in the list. Finding the average of three numbers A, B and C would involve forming the sum A + B + C and dividing by 3. It answers the question “If all quantities had the same value, what would that value have to be in order to achieve the same total?” and the calculation is relevant whenever the quantities concerned add together to produce a total. For instance, if you buy milk, bread and butter you will be expected to pay a total sum to cover the price of these three items and calculating the average would tell you what price a different product X would have to have so that you could buy three instances of X and end up paying the same amount.

The trouble with the simple average is that is greatly influenced by outliers, i.e. extreme values at either end of the spectrum. If you calculate the average of ten 5s and 1000 you will end up with (10 * 5 + 1000) / 11 = 95.45 which is unproportionately large and could give the impression (assuming the individual data points are not known) that the data is concentrated around values just short of 100. This problem is a simple example of skewed distributions where the mean of a data series doesn’t coincide with the median (the “middle value” if you were to list them all).

Finally, the arithmetic mean is not suitable for calculating stock performance since you’re looking for the product of the yearly performance, not the sum of those values. Consider an investment that loses 10% of its value in the first year and gains 30% in the second year. Now the annualised performance since you started investing is not [(-10%) + 30%]/2 = 10% but in fact 8.2% since the 30% increase only affects the 90% of your investment that’s left after the first year. To correctly calculate annualised performance rates like this we will have to use the geometric mean.

Excel Function: AVERAGE(number1, [number2], …)

Geometric Mean

The geometric mean is a value that gives an indication of the central tendency of a set of numbers (i.e. of a distribution) regardless of whether this distribution is normal or skewed. In other words, it shows the “typical value” of a list of values. Note that this is different from the most common value which is a mathematical value called “mode”. It answers the question “If all quantities had the same value, what would that value have to be in order to achieve the same product?” and hence is relevant whenever quantities multiply together to produce a product. The geometric mean is always less than or equal to the arithmetic mean.

To calculate the geometric mean you need to multiply all the values in your set and subsequently find a scientific calculator to take the nth root of the product where n is the number of numbers you previously multiplied. In the simplest case when calculating the geometric mean of two values A and B you would need to take the square root of A*B. Unfortunately, this also means that the geometric mean in its purest form can only be applied to positive values as (in conventional mathematics and without exploring imaginary values) you cannot take the root of a negative number.

While we all hope that our investments are going to increase year after year, we can’t simply assume this and happily apply the geometric mean without a little work first. To take negative growth into account, you will need to look at your percentage values from a slightly different angle. Let’s go back to our original example of a return of -10% in the first year and 30% in the second year. After the first year, only 90% of your original investment will remain - that is, your portfolio will stand at 0.9 instead of 1 (= 100%). In the second year, you’re more lucky and see a 30% growth of that remainder. If you would have had a fresh portfolio (i.e 100% = 1) you’d now be left with 130% of your money or 1.30. Since you only had 90% remaining we need to multiply 0.9 by 1.30 to get 1.17. This means that in relative terms to the amount you started with, your investment is worth 17% more after 2 years. To now calculate the annualised growth rate of your investment we need to take the square root of 1.17 which yields 1.0816 or a growth of 8.16% per annum.

The Excel function given below does not convert your percentages accordingly so the restriction with regards to positive values still applies. So far, I haven’t been able to find an in-built function that does the work for you which I find rather frustrating. It is extremely annoying to represent a 10% drop in my portfolio as 0.90 and if I don’t come across a more workable solution soon, I will probably end up writing a function myself If you know something that I don’t please let me know before I spent hours writing an Excel Add-In from scratch.

Excel Function: GEOMEAN(number1, [number2], …)

Frequency Distribution

If you’re a visual thinker like myself, you will appreciate that I often find it more helpful to look at a graph instead of raw numbers. An obvious choice in the case of portfolio returns is a histogram which is based on a frequency distribution. At this stage, I won’t dwell on this topic for long as I haven’t got sufficient data yet to experiment with histograms and the associated frequency distributions yet. As soon as that is the case, I will almost certainly give you a little more insight into this topic.

For the moment, imagine that you have two buckets in which you need to throw little cards that represent your portfolio performance - whether you’re looking at weekly or monthly returns or any other values is fairly irrelevant as long as you have enough data. Your task now is to separate the positive returns from the negative ones by throwing them into their respective buckets. Once you’re done with that, you can draw a simple bar graph with the number of items per basket representing the height of an individual bar (assuming one unit width per bar). Voila - there is your first histogram

If you imagine that you could have as many buckets as you like, then you only need to come up with a criteria to decide which bucket contains what data to create whatever histogram you like. You could distinguish between negative and positive values, determine 5% steps or pick any other classification you might find useful. The only rule is that categories must not overlap - i.e. there is always one unique bucket for every single piece of data and at no point would any value (whether in your sample or not) match two or more buckets.

The interesting thing about histograms is that it’s not technically the height of a bar that determines the value it represents (unlike in a simple bar chart where only the height matters) but it’s the area that is covered by it. Hence you could draw a bar that’s one inch wide and three inches high and that would represent the same value as a bar that’s three inches wide and one inch high. For this reason the bars of a histogram have to be adjacent with no gaps in between.

Because you are free to choose however many buckets you want to use when constructing a histogram (the official term for my made-up bucket is “bin”) much research has been done to determine the optimal number of bins as too small a number might hide valuable insights while too many bins render the diagram useless. The level of granularity is crucial. One formula that has been put forward is k = [(max(x) - min(x)) / bin width h] where k represents the optimal number of bins and max(x) and min(x) denote the maximum and minimum values of your data respectively. Whatever value you calculate, you should round up to the nearest full value and use this to create your categories.

Excel 2007 includes an Add-In that creates a histogram from your data if presented in the correct way (data values in one column, bin limits in second column) and hence extends the basic FREQUENCY function that simply returned an array of values. While I have Excel 2007, the data arrangement it requires to execute properly doesn’t work very well if you’re planning to have more than just a histogram graph in your worksheet. Further, from the previews I have seen of the functionality, the histogram looks wrong as there are in fact gaps between the bars (which violates the rules given above). Hence, once more I find myself wondering whether I should invest the time and effort to create something a little more elegant myself. Stay tuned

Maximum and Minimum Value

Since I assume you graduated from primary school long ago, I don’t really need to explain the meaning of maximum and minimum value to you. I simply include it for completeness’s sake and to create a central place for all important Excel functions

Excel Function: MAX(number1, [number2], …) and MIN(number1, [number2], …)

Positive and Negative Number of Weeks

This is an interesting little insight I came across in the book I was reading about Asset Allocation not long ago. While it doesn’t tell you that much per se, it gives you valuable perspective and a sense of patience when you’re tempted to give up your long-term investing for short-term speculation. If you can see that your investment is up most weeks / months / years and only down in value occassionally, you might find it easier to sit out the rough patch - rest assured that other (better) times will come.

To avoid having to count these items manually every time you update the performance, you can use the Excel function COUNTIF that looks at a list of values and only counts the instances that fit a criteria given as part of the formula. By using the criteria “>0″ you will end up with a count of all positive values, while “<0″ returns a total of negative occurences.

Excel Function: COUNTIF(range, criteria)

I hope you enjoyed this first introduction into maths and basic statistics as I very much look forward to researching the upcoming posts! If you have any questions or concerns, just leave a comment and either myself or another reader will surely be able to help.

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