A large group of my students sat an exam last Saturday. This was for the Chartered Financial Analyst (CFA®) Program, which has exams with a reputation for being somewhat challenging, to say the least. The pass rates have been between 34 and 46% for a number of years, providing success only to those who commit themselves for a number of months prior to the exam.
For the most part, it is fairly straightforward for us, as classroom tutors, to tell prior to the exam which of our students are likely to succeed and which ones won’t, for the simple reason that with 240 multiple choice questions, there is remarkably little luck involved (a statement that would be highly disputed by many students I know!).
However, at what point has a successful student passed and an unsuccessful one failed? On the day of results, or earlier?
Exam results nerves
People of my tender age will remember O-level and A-level exam results arriving at home in a small brown envelope, back in the days when next-day postal deliveries were guaranteed. The envelope was always addressed in my own handwriting, the address being written with extreme care, given my calligraphically-challenged reputation. But when were my exam results decided? When I opened the envelope? Surely earlier than that. When the envelope was posted? When the results slip was put inside? When the exam was marked? As soon as I had walked out of the exam hall? Or even earlier, maybe when I walked into the exam hall?
Most people would agree that the result is determined at some point between the start of the exam and the results becoming known to the candidate.
Let’s consider a point in time just before results are published – these days via the internet. It seems clear that the examiner has already decided results, but is checking the database and the computer system before pressing SEND.
The majority of candidates are unsure whether they have passed or failed. A confident student may feel they have an 80% chance of success. But how does probability come into it, when the result has already been determined?
Schrödinger’s Cat
Without going into the details of quantum mechanics, let me summarise the fate of Schrödinger’s Cat. Austrian physicist Erwin Schrödinger proposed a hypothetical experiment in 1935 in which a cat was placed in a perfectly sealed container. In with the cat was a radioactive device that, with a specified probability, say 50%, would trigger the release of a poison that would kill the cat *.
Because the container is perfectly sealed, no noise, or in fact any information, can travel from the inside to the outside (one must assume a sufficient oxygen supply for the poor, albeit hypothetical, creature). Hence at the specified moment in time, the cat could be either alive or dead.
Schrödinger suggests that the cat is not “either alive or dead” – rather, it is both alive and dead simultaneously. The cat is potentially in two separate overlapping existences at the same time.
It is only when the box is opened that one of these two states is crystallised, and the other vanishes from our own field of view.
The cat and the exam
Now we can apply the analogy of Schrödinger’s Cat to exam results.
Immediately prior to opening the envelope / logging on, one can consider the results as being in two simultaneous states with two probabilities. Each candidate will have different probabilities, depending on their perceived performance.
I use the word “perceived” because the more information that is available, the more skewed the probabilities are. A candidate may think she has a fair chance, say 60%, of passing. As a tutor I may have observed several months of hard work, bringing the probability up maybe to 80%. A theoretical snapshot of her exam paper, and knowledge of how the pass score is determined (I suppose the equivalent of having a secret camera in the container with the cat), may bring the probability up to 100%. Of course, it might instead reduce it to 0%!
Our students are now relaxing, hard work over, and starting an eight-week period of blissful ignorance before the dreaded results arrive. However unsure they may be of what will be inside the little brown envelope, one thing is clear: uncertainty doesn’t come into it.
* No animals were harmed in the creation of this blog entry.
Thursday 10 December 2009
Thursday 25 June 2009
Why low interest rates are good for savers
Many articles in the popular press have admonished banks and building societies for passing on base rate cuts in full to savers, reducing savings interest rates to pretty well zero.
In fact when you consider the true value of your savings, low rates in fact can benefit savers quite significantly.
In fact when you consider the true value of your savings, low rates in fact can benefit savers quite significantly.
The basis of my claim is the Fisher effect, which in broad terms says that interest rates and inflation rates move roughly in line.
Let me define the real interest rate as the increase in purchasing power at the end of a year. For example, suppose interest is 5% and inflation is 3%: at the end of the year you can afford roughly 2% more goods. (This is a slight approximation, but for small numbers it’s pretty close.) This 2% is the real interest rate. The actual 5% paid by the bank is called the nominal interest rate.
If inflation were to rise, typical monetary policy would be to increase rates. This would increase both our mortgage cost and the reward for savings, the combination of which discourages us from spending. Hence we look for better value, prices are kept down and inflation is kept at bay. By contrast, were inflation to fall, interest rates could safely reduce, allowing us to spend more without prices skyrocketing. You can see from this description that interest and inflation rates are likely to move broadly in the same direction, confirming to some extent the Fisher effect.
Let us consider a saver, Jane Bloggs, who has £100,000 in the bank. She receives the interest and uses this as income. Consider a number of scenarios that stick to the Fisher concept. Each scenario will use a real interest rate of around 2%, with nominal interest rates remaining at 2% more than inflation.
Firstly, suppose nominal interest rates are 2% and inflation is 0%. Jane receives £2,000 per year, leaving the £100,000 principal untouched. In real terms (i.e. incorporating inflation), the principal remains the same, as prices haven’t moved.
Now let interest rates rise to 5% with 3% inflation. The income is now £5,000. Should Jane spend all of this, the remaining £100,000 is now worth approximately 3% less in real terms at the end of the year, as prices have gone up by this amount. Should she instead spend only £2,000 of her interest, then £103,000 remains. This has the same spending power as the £100,000 at the start of the year (an item that used to cost £100 now costs £103). Note the similarity: if £2,000 is spent, the value of principal in real terms remains the same.
What if rates fall? Let’s say interest rates are zero and inflation is minus 2%, i.e. there is 2% deflation. Jane can again spend £2,000: the principal is now £98,000, which has the same real value as before (an item that used to cost £100 now costs just £98).
Conclusion: regardless of what the nominal interest rate is, the 2% real interest rate is what Jane can spend without losing the spending power of her savings.
A dose of reality: here comes the taxman
As it happens, Jane pays 40% tax on all interest. (For a 20% taxpayer the effect is similar to what follows, though to a lesser degree.) Let us review the scenarios one by one, starting with the highest rates.
Interest 5%, inflation 3%. Jane receives £5,000 interest, from which £2,000 tax (i.e. 40%) is removed. Her bank account shows £103,000 before any cash withdrawals, and this exactly matches inflation. In other words, her savings have exactly kept up with inflation, but she may not spend a single pound without losing real value.
Interest 2%, inflation 0%. Jane’s £100,000 now receives £1,200 interest (£2,000 minus 40% tax). She can happily spend the £1,200, as the principal maintains the same value in real terms. In other words, she has made 1.2% in real terms.
Finally interest 0%, inflation minus 2%. With zero interest, Jane suffers not a single penny of tax. As we saw above, Jane can withdraw £2,000, leaving £98,000. In real terms the principal is unchanged, and she has spent £2,000.
As these examples show, the higher the rates are, the worse off Jane is – see the diagram (which shows Jane’s position with a 2% real rate and 40% tax) for the impact. With rates above 5%, Jane’s real return is actually negative, giving her less spending power at the end of the year than at the start. Provided the Fisher effect is legitimate, savers are better off with low rates than high rates, as long as they keep their eye on the real value of their savings and not the nominal value.
In case you’re still not convinced and yearn for higher rates, my prediction is that inflation (and, with it, interest rates) will rise significantly within a year. This could be the result of many factors, including:
1. The government will need inflation to remove the (real) value of the incredible amount of debt that has been incurred in the last few years;
2. Quantitative easing will have an impact on credit creation, allowing people to borrow (and spend);
3. Recent reductions in manufacturing output will lead to higher prices when we finally start spending again (since shops, motor showrooms and factories won’t have enough stock); and
4. Oil prices, being double what they were four months ago, have pushed up manufacturing and motoring costs, and will take inflation with it.
I would hope that most savers will see the problems associated with higher interest rates for what they are, and be glad that their banks, by paying them low rates, are in fact doing them a service.
Wednesday 24 June 2009
Public Sector Pensions – a Ponzi time bomb for the taxpayer
The 2008-09 credit crunch / banking crisis is of significant concern to almost all of us. Is our job secure? Are our savings safe? What will tax rates be next year? Am I now in negative equity on the house? By how much have my pension expectations been crushed?
To those of us in our 20s or 30s and not working in finance, pension expectations may seem rather less pressing an issue than losing our job next week. However if you really think that pensions are something you can sit back and ignore till your 50s, you're wrong.
Types of pension plan
There are two broad categories of pension plan: defined benefit (or "final salary") and defined contribution (or "money purchase").
In a defined benefit plan, the employer provides a guarantee of a post-retirement income for former employees. This is usually based on salary and length of service and typically will be of the form "X% of final salary multiplied by years of service". If, for example, X% is 2%, then a staff member retiring after 30 years of service will receive 60% of their final salary as a pension.
The plan will have assets and liabilities: the assets are the investments (shares, bonds, property, etc), while the liabilities are today's estimate of future pension payments.
More and more defined benefit plans have now closed, as they can prove rather expensive. Pension plans are often bigger than the company itself: the British Airways pension fund has liabilities some 6.5 times bigger than BA's market value.
The benefits of such plans vary widely, ranging typically between one-eightieth and one-fiftieth of final salary per year. For instance, 40 years of service on a one-eightieth multiple will get 40/80 or half of final salary as a pension income.
A defined contribution plan is rather simpler to describe: the employee and/or employer pay a fixed amount, usually a percentage of salary, and this is invested on the markets. The pensioner's income will then depend on how the investments perform.
The key difference between the plan types is who takes on the risk: for defined benefit, the employer bears the risks; while members of a defined contribution plan take on the risk of poor market performance themselves.
How big is my pension pot?
Quite likely, not as big as it needs to be. Let's do a simple example.
Consider each £1000 of annual salary. Ignoring who bears the risk, suppose an employee wishes to build up a pension income of 60% of final salary after thirty years of contributions - i.e. one-fiftieth per year. This means that the £1000 income this year will provide an annual income of £20 per year (£1000 ÷ 50) after retirement. At today's rates you'll need investments of at least £500 to achieve £20 of income. In other words, for each £1000 of your current salary, you need to save £500.
Go on - hands up if you pay 50% of your salary into your pension?
Exactly, I didn't think so.
What about the public sector?
A close family member retired a few years ago from a career in one of the government departments. He is now receiving a comfortable index-linked pension. After 30 years at Her Majesty's service, how big is the pension fund that pays his monthly income? Precisely zero.
Most public sector pensions are unfunded, meaning that they are paid from current budgets. In other words, today's taxpayers are paying today's pensions. With current employees not receiving their pension until later this century, their future pensions are certainly not this government's problem!
Let's get the scale right: we're looking at somewhat over £650 billion of public sector pension liabilities according to the BBC's Robert Peston, or around £25,000 per person paying UK income tax. Newspapers have bandied around various eye-popping headlines over how much debt we're all in now - the £25,000 per taxpayer is not the national debt, nor the impact of the credit crunch. It is the amount that each taxpayer - public and private sector - owes just for public sector pensions.
The Ponzi time bomb
Bernie Madoff, eat your heart out. The government has created the Ponzi scheme of all Ponzi schemes, too big even to shake a stick at.
Named after the 1920s fraudster Charles Ponzi, such a pyramid scheme promises unrealistic returns, with early investors being paid out from subsequent investments rather than from profits. In order to survive, the scheme must continue to grow exponentially, though it is destined to collapse eventually.
Typifying the short-termism of the current government's budgetary control is the Royal Mail pension plan. This scheme has serious problems: assets of £20 billion, but liabilities some £9 billion higher. Such a shortfall would cause problems for any pension fund manager. However the government has created what seems like a much neater solution. The assets will be absorbed into today's deficit, reducing national debt. In other words, "We've already spent it". The near £30 billion of liabilities will be added to the £650 billion, leaving the problem for the next generation and certainly the next government.
The UK's public sector pension mountain is not unique - in fact Schwarzenegger's problems with Californian police and firefighter pensions are well reported. European pension imbalances are considered by some a threat to the euro currency itself. In fact most developed countries (Singapore being the shining exception, with a fully funded scheme for all eligible citizens) must come to grips with the fact that (1) people are living longer, (2) people are reluctant to retire later, and (3) stock market returns are not predictable.
A solution?
Sadly, the only solution that would have a real impact is politically and socially impossible.
Private sector pensions can be modified or reduced without much political backlash. Towards one end of the spectrum are Enron and Equitable Life. But other radical changes have taken place, even very recently: in just the last week we have seen BP close its defined benefit scheme to new employees, as well as Barclays moving existing employees from DB to DC. Such changes are politically unpalatable in the public sector.
Should a government have the willpower, new civil servants should move to a defined contribution plan, at the very least. This is the "BP solution". This will cost more (yes, payments will be needed today, not when today's new recruits retire), but the impact is gradual. In fact so gradual that the benefits will only be realised in the second half of the century.
Somewhat more radical would be the "Barclays solution", changing benefits for existing employees, keeping the defined benefits they have already earned, but using a defined contribution plan from now onwards. This would mean changing employment contracts and would cause a legal minefield. Again, most budgetary benefits would be decades away.
Most radical of all would be to backdate a reduction in benefits. Although this would have an immediate reward for the chancellor's books, it would represent political suicide for any government attempting such a move.
There are no easy or palatable solutions. As public sector pension liabilities continue to grow, it will take a strong government to prevent them from ballooning even further out of control.
Whoever is in power next year, they have a tough job ahead.
For the rest of us: invest wisely, don't believe financial forecasts, and, above all, sit tight.
To those of us in our 20s or 30s and not working in finance, pension expectations may seem rather less pressing an issue than losing our job next week. However if you really think that pensions are something you can sit back and ignore till your 50s, you're wrong.
Types of pension plan
There are two broad categories of pension plan: defined benefit (or "final salary") and defined contribution (or "money purchase").
In a defined benefit plan, the employer provides a guarantee of a post-retirement income for former employees. This is usually based on salary and length of service and typically will be of the form "X% of final salary multiplied by years of service". If, for example, X% is 2%, then a staff member retiring after 30 years of service will receive 60% of their final salary as a pension.
The plan will have assets and liabilities: the assets are the investments (shares, bonds, property, etc), while the liabilities are today's estimate of future pension payments.
More and more defined benefit plans have now closed, as they can prove rather expensive. Pension plans are often bigger than the company itself: the British Airways pension fund has liabilities some 6.5 times bigger than BA's market value.
The benefits of such plans vary widely, ranging typically between one-eightieth and one-fiftieth of final salary per year. For instance, 40 years of service on a one-eightieth multiple will get 40/80 or half of final salary as a pension income.
A defined contribution plan is rather simpler to describe: the employee and/or employer pay a fixed amount, usually a percentage of salary, and this is invested on the markets. The pensioner's income will then depend on how the investments perform.
The key difference between the plan types is who takes on the risk: for defined benefit, the employer bears the risks; while members of a defined contribution plan take on the risk of poor market performance themselves.
How big is my pension pot?
Quite likely, not as big as it needs to be. Let's do a simple example.
Consider each £1000 of annual salary. Ignoring who bears the risk, suppose an employee wishes to build up a pension income of 60% of final salary after thirty years of contributions - i.e. one-fiftieth per year. This means that the £1000 income this year will provide an annual income of £20 per year (£1000 ÷ 50) after retirement. At today's rates you'll need investments of at least £500 to achieve £20 of income. In other words, for each £1000 of your current salary, you need to save £500.
Go on - hands up if you pay 50% of your salary into your pension?
Exactly, I didn't think so.
What about the public sector?
A close family member retired a few years ago from a career in one of the government departments. He is now receiving a comfortable index-linked pension. After 30 years at Her Majesty's service, how big is the pension fund that pays his monthly income? Precisely zero.
Most public sector pensions are unfunded, meaning that they are paid from current budgets. In other words, today's taxpayers are paying today's pensions. With current employees not receiving their pension until later this century, their future pensions are certainly not this government's problem!
Let's get the scale right: we're looking at somewhat over £650 billion of public sector pension liabilities according to the BBC's Robert Peston, or around £25,000 per person paying UK income tax. Newspapers have bandied around various eye-popping headlines over how much debt we're all in now - the £25,000 per taxpayer is not the national debt, nor the impact of the credit crunch. It is the amount that each taxpayer - public and private sector - owes just for public sector pensions.
The Ponzi time bomb
Bernie Madoff, eat your heart out. The government has created the Ponzi scheme of all Ponzi schemes, too big even to shake a stick at.
Named after the 1920s fraudster Charles Ponzi, such a pyramid scheme promises unrealistic returns, with early investors being paid out from subsequent investments rather than from profits. In order to survive, the scheme must continue to grow exponentially, though it is destined to collapse eventually.
Typifying the short-termism of the current government's budgetary control is the Royal Mail pension plan. This scheme has serious problems: assets of £20 billion, but liabilities some £9 billion higher. Such a shortfall would cause problems for any pension fund manager. However the government has created what seems like a much neater solution. The assets will be absorbed into today's deficit, reducing national debt. In other words, "We've already spent it". The near £30 billion of liabilities will be added to the £650 billion, leaving the problem for the next generation and certainly the next government.
The UK's public sector pension mountain is not unique - in fact Schwarzenegger's problems with Californian police and firefighter pensions are well reported. European pension imbalances are considered by some a threat to the euro currency itself. In fact most developed countries (Singapore being the shining exception, with a fully funded scheme for all eligible citizens) must come to grips with the fact that (1) people are living longer, (2) people are reluctant to retire later, and (3) stock market returns are not predictable.
A solution?
Sadly, the only solution that would have a real impact is politically and socially impossible.
Private sector pensions can be modified or reduced without much political backlash. Towards one end of the spectrum are Enron and Equitable Life. But other radical changes have taken place, even very recently: in just the last week we have seen BP close its defined benefit scheme to new employees, as well as Barclays moving existing employees from DB to DC. Such changes are politically unpalatable in the public sector.
Should a government have the willpower, new civil servants should move to a defined contribution plan, at the very least. This is the "BP solution". This will cost more (yes, payments will be needed today, not when today's new recruits retire), but the impact is gradual. In fact so gradual that the benefits will only be realised in the second half of the century.
Somewhat more radical would be the "Barclays solution", changing benefits for existing employees, keeping the defined benefits they have already earned, but using a defined contribution plan from now onwards. This would mean changing employment contracts and would cause a legal minefield. Again, most budgetary benefits would be decades away.
Most radical of all would be to backdate a reduction in benefits. Although this would have an immediate reward for the chancellor's books, it would represent political suicide for any government attempting such a move.
There are no easy or palatable solutions. As public sector pension liabilities continue to grow, it will take a strong government to prevent them from ballooning even further out of control.
Whoever is in power next year, they have a tough job ahead.
For the rest of us: invest wisely, don't believe financial forecasts, and, above all, sit tight.
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