SAVING MONEY - WHY AND HOW
(1) The first step in the investing process is saving money. There is no way around this. You can try to avoid it by buying lottery tickets, or playing penny stocks, or day-trading, but the chances these strategies will grow your nest-egg are slim-to-none. It is more likely that you lose all you started with.
Investing is not 'a way to make money'. You work a job to make money. Investing does not create wealth. It only earns a percent-return on the principal. When your savings are small, the dollar-return from investing will always be small.
At the start, each additional dollar saved is far more effective in growing your wealth than any increase in the percent-return. You double your dollar-returns by doubling your total $$ saved, not by assuming the risks of investments promising sky-high percent-returns.
Say you earn $40,000. Compare the different rates of return you must earn from your savings, to end up in the same place after 10 years, if you save 10% v. 12% of that $40,000. Saving only 2% less from your wages, forces you to earn (and assume the risk) double the rate of return on those savings. Prove this to yourself using the FV of Annuity function of your financial calculator (Problem #3).
|Earn $ ||Save % ||Save $||Invest % ||End with |
|$40,000 ||12% ||$4,800 ||4% ||$57,629 |
|$40,000 ||10%||$4,000 ||8% ||$57,629 |
The media refutes this by repeating the argument: "Mutual fund commissions will destroy your long-term wealth. Those 2% fees each year have a HUGE impact". Therefore investors conclude they must sweat every additional 2% additional return they possibly can.
Yes, their math is correct, but they predetermine their results two ways. They either presume the investor STARTS with a large portfolio, or they measure the ending value after such a long period of time, that for most of the time the portfolio has been quite large. Rates of return DO matter when you already have a $50,000 portfolio. They do NOT matter when you are saving your first $20,000 for a home's downpayment.
Look at the example above differently. Consider the reduction in return from safe investments an expense - as a cost of buying insurance against poor portfolio returns on the risky investment. Measure that cost as a percent of your income - not a percent of the portfolio's value - to see how easy it is to afford. 4% of a small $10,000 portfolio is only $400 a year - about $1 per day. That is affordable by most everyone. But for the older person with a $800,000 portfolio, that insurance equals $32,000 - almost a full year's pay. Conclusion - buying portfolio insurance is affordable when your portfolio is small, but not affordable when it is larger. Young people should be satisfied with the safer investments.
But, you are saying, in 2009-2010 savings do not return 4%. They return only 2%, so this argument is invalid. In low rate environments, all returns get impacted. The choice becomes not 2% vs. 8%, but 2% vs. 6%. Stock and other investments are very highly priced in 2009-2010 precisely because of the low rate environment. The point of the argument remains the same.
(2) The strongest reason for saving money is that by deferring gratification you vastly magnify the gratification you receive later in time. You must always pay for your purchases, either cash upfront or paying down debt later. The sum of payments necessary to get rid of debt are many multiples of the cash payments set aside into savings before you buy.
Say you want to buy a yacht for $150,000. You can choose to wait for 13 years while saving up $194,033 ($150,000 plus inflation) or you can buy now using debt and spend 40 years paying down that debt. Yes, 13 years may seem like a long time to defer gratification, but consider the benefit. For the subsequent 27 years the borrower must continue those payments while the saver can put that money aside for another purchase. If invested, those same cash flows can grow a retirement portfolio of $621,131.
So, you don't plan on buying a yacht. The same principle applies to buying a car with debt, or taking a vacation before saving for it, or even buying the Christmas presents on credit. This example pays down a large debt, but many families carry a $50,000 credit card balance perpetually. That is just as onerous.
(3) The reason to start saving early is because it will cost you a lot more if you delay. You may have heard advice like "If you start saving for retirement at age 35 you only need to save 15% of your wages, but if you only start in your 30's you need to save 20%". Or some such statistic. It is a lot worse than that. The following chart shows that a 10 year delay will require you to triple your savings in order to make up the difference. Granted the chart assumes a steady $$ of savings, while most people will be able to increase their savings at least with inflation. The spreadsheet for determining How Much You Need To Save will confirm that a 10 year delay using the default variables causes the required savings to rise from 10% of salary to 27%.
DON'T ASSUME RISK
Assuming the risk of investments when your savings are small accomplishes nothing. There are seven arguments supporting high risk investing for young people - and counter-argument.
Many wealthy older people profiled in the media partially attribute their success to a lucky windfall when they were young - a windfall that funded their future adventures. Of course, all the other people who tried the same thing, but did not get the lucky break, never end up being profiled in the media. You do not hear about them, but they will have lost all their savings, and may have continued to lose any subsequent savings their whole life. Risky investments create few winners, but many losers.
Risk can be defined as the probability of losing your principal . The argument is made that a young person can handle this risk better than an older person. If a young person's principal is lost he still has plenty more years of working salary from which to replace it. This idea of human capital says you should count as an asset the present value of your future wages. This large stable asset of a young person would offset most risk taken in the market. The retired person must invest more safely because he has no human capital.
Ayres and Nalebuff go even further to advise that the young should go into debt to increase their equity exposure to greater than 100%.
There are two counter-arguments. First - replacing savings lost in risky investments may be harder than anticipated. You may lose your job, or get divorced, or have triplets, or get sick. These events can force you to sell losing investments - locking in losses - and go into debt. Having a paycheque may not be sufficient to save you.
Second - the risk profiles of retired vs. young people may not be so different. Most peoples' retirement income comes from guaranteed government benefits and pensions - not portfolio returns. These are equivalent to the safe human capital of young people. So young people's risk profile is not really different.
Risk can be defined as the volatility of the investment's price. A young person can handle this risk better than an older person. Retired people need certain cash to pay the bills. Any declines in the value of their investments, even temporary ones, are crystallized when the retiree has to sell at that lower value. The young person has a longer investing horizon. He does not need certain cash. He can ignore temporary declines and wait for the longer term gains.
The problem with this argument is that young people are not saving for retirement. They save to fund the first and last month's rent when they leave home. They save to buy a car; to pay off their education debt; to buy an engagement ring; for a real-estate downpayment. These purposes require certain cash in the same short timeframe that the retiree faces.
Today's reality is that these purchases will be made even if there is no savings, by going into debt - the first really big financial mistake of a life. That is what will happen if the risky investment goes sour.
It can be argued that a (say) 20 percent loss will hurt the person with a large portfolio more than a young person because that percentage will be much larger in actual dollars. It will be easier for the young person to replace the $$dollars, so he can assume more risk.
The problem with the comparison is that values are being compared at different points in the portfolio's growth over time. Instead, consider the small $$ loss of a teenager as a permanent loss of 'seed capital' - seed capital that would have grown over time to become much larger. It is the future value of the current loss that should be compared to the retired person's loss.
There is a common argument that volatile, risky investments become LESS risky when considering a longer time horizon. This idea was effectively argued against by John Norstad. This is discussed in detail in the Risks page.
It is argued that by sequencing your savings' objectives over your life, with retirement savings after paying for purchases and real-estate, your exposure to the stock market is limited to the last short period of your life, and this exposes you to the vagaries of chance. This risk could be reduced by investing for a much longer period of time - by using debt if necessary - by choosing to invest instead of paying off the mortgage. This table from Crestmont shows clearly how average returns are moderated with longer horizons.
But that table ignores savings added during the investment period. Even when savings are started young, market returns at the end of the period have more impact because of the larger portfolio. The chart above shows how little dampening there is with even an additional 10 years of savings. Also, this US data reflects a cyclical stock market that does not exist in Canada. The additional 10 years of savings would make even less difference here.
- There is an ages-old asset allocation rule of thumb that says your portfolio should hold Your Age In Bonds. In other words, the 20-year-old should own only 20% bonds, but that should increase so that the 60-year-old would hold 60%. This rule in effect says young people should take on more risk.
Research Affiliates did a back-test of the Glide Path strategy which similarly increases the proportion in debt as the retirement date approaches. Using historical data they assumed a steady savings$ that was invested proportionally in equities and debt. At retirement they calculated what annuity income the resulting wealth would buy. They found that results were better when the Glide Path was reversed - when the bond proportion decreased. Not only did the average outcome improve, but there was little-to-no additional downside risk from the lower range of possible outcomes.
This finding was validated by Estrada (2013) when working with US as well as international data. Not only were the mean and median ending values higher when the glide-path was reversed, but the worst-case scenarios were less bad, and the up-side potential was greater.
Other strategies were also compared. Results were better when a 60:40 (equity/debt) allocation was maintained throughout. Results were even better when equities were kept at 100% for the first few decades - even when bonds were added in the last decades.
The problem here is that this models an index investor with nerves of steel and no personal needs along the way to raid the piggy-bank. In real life, the young investor will probably not use a passive strategy, he will probably freak out after large stock crashes, he may lose his job and raid his savings, etc. What works in theory won't work in practice.
Theoretically, while the Reverse Glide Path strategy is more likely to surprise investors with a bigger drop in value at the end of the investor's working life, this potential higher drop is more than offset by earlier larger gains. In real life, investors look at their large portfolios and become complacent about savings. They make plans based on this pot of wealth. If it loses half its value just before retirement they will feel very real pain.
- Maybe the most convincing argument for assuming risk while young is that it gets that necessary phase out of your system. It is probable that most investors lose money early on ... and that those losses teach a lesson. The research into the returns earned by retail investors shows poorer results for small accounts and younger investors. Those losses are probably the result of risky lottery-like behavior.
Those with savings managed for them all their lives inside retirement accounts frequently decide they are qualified to be stock-pickers as soon as they get control of the account at retirement. They jump right in with no experience. They are likely to be attracted to 'the big payoff' just like inexperienced youth, putting at risk their life-time of savings. It would have been much better for them to have 'learned the lesson' of risky investing while young and got it out of their system.
YOU DO NOT SAVE BY GOING INTO DEBT
Obviously? The proof that many people do not understand is in the "financial makeovers" that magazines love to publish. The issue also shows up on financial discussion forums. Lots of people have 'savings' funds at the same time they carry consumer debt (credit cards, auto leases or loans, lines of credit, education debt). They chose to NOT pay their bills and put the cash into 'savings' instead.
This is self-defeating because the interest rate on personal debt will inevitably be far higher than the return earned by the savings. Also consider the different risks. Your debt is certain, but your investment income will have some risk attacked. Also consider taxes that reduce the income from savings, but allow no relief from the debt's interest. You should always analyze investments on an after-tax basis. The math is simple. Multiply the nominal return by the factor (1 minus your marginal tax rate). For example, if the GIC earns 5% and your marginal tax rate is 30%, the after-tax return is 5% * (1-.30) = 3.5%.
This situation results from five common mistakes.
- People do not create an emergency fund with ready cash. Everyone's life throws up unexpected expenses. The last thing you want to happen, then, is to augment the problems with the added burden of debt. But when all your savings are invested in long-term securities or behind government sponsored savings plans, these expenses will be paid for with debt.
Savings plans are now funded by automatic bank transfers. It is felt that this automation of the process takes away the risk of frittering away the cash. People think that if the cash is not in their chequing account it will not be spent. Not true for many people. They simply make the purchase with a credit card.
True savings requires a deferral of gratification. You chose to NOT spend now in order to generate greater gratification in the future. You only save by spending less than you earn, not be automatic bank transfers. Saving is what is left AFTER ALL THE BILLS ARE PAID.
There was an influential book called 'The Wealthy Barber'. It coined the phrase "pay yourself first". The author presented the concept as a substitute for budgeting - which he acknowledged did not work. What he meant by the phrase is "set aside a predetermined $ savings before deciding what else you want to buy". He assumed that people would not spend money if it was not in their account. But the public has wrongly interpreted his advice to mean "set aside a predetermined $ savings before deciding what purchases to pay for".
Another misinterpretation, even worse, tells people that "pay yourself" means "give yourself a treat" each month, before setting aside savings. This is like giving your dog a treat BEFORE asking for the obedience. Not likely to generate the desired behavior.
Governments give tax breaks to promote savings for retirement. To benefit from these breaks you must move your money behind a kind of firewall. It is hard to get the money out later without incurring taxes and penalties. Young people are encouraged to use these schemes without considering that their savings are not for retirement, but for foreseeable purchases. The result is that those purchases are paid for with debt.
Being in debt is so common in society that familiarity breeds nonchalance. Everyone does it so it must be OK. Paying for a car is now rare. Buying 'aspirational' brands is considered necessary for our emotional well-being. Sweating the small stuff is a negative personal attribute. The value of things are determined by their price tag.
HOW TO SAVE
Spend less than you earn. This should be a habit for life. Even in retirement you cannot spend all your pension income because some of it needs to be reinvested to compensate for the erosion from inflation, and to cover unexpected medical costs. Although the rate at which you save will change with your paycheque and your mortgage balance and if your kids are in university, you should always live below your means. A (very) rough rule of thumb is to save 25% of your gross paycheck. 15% of that should increase your net wealth, i.e. saved for retirement through investments or growing the equity in your home (yes, that is saving). The other 10% should be saved for future consumption e.g. a replacement car, a wedding, new washer/dryer, travel, etc. This may sound like overkill. But it is not much different from living with unpaid consumer debt. If you end up never spending that 10% for consumption, you can retire early.
If you cannot keep track of what you have spent because the costs are hidden until the credit card statement comes, stop using credit cards. Yes it is that simple. Take them out of your wallet. Stash them in a drawer until you are making a specific trip to buy (e.g.) car insurance that would be an appropriate card transaction. Or keep a card in your car's glovebox (well hidden and with a credit limit of only a few hundred dollars), so that it will be used only for necessary gas. Or freeze them in a block of ice, so that you must stop and thaw before they can be used. Learn what your emotional triggers are. Then figure out ways to bypass them.
Build walls around your savings if you find them too tempting. If the existence of a pot of cash triggers thoughts of vacations or new cars, make use of mental trickery. Keep the savings in your brokerage account instead of your chequing account. Keep a second bank account dedicated to ONLY some stated purpose. Invest inside an RRSP instead of a TFSA, even though you expect your tax rate on withdrawal to be higher. Choose automatic DRIPS of dividend income. These might not be optimal decision otherwise, but if they promote your savings, then their 'cost' is worth it.
Purchase discretionary items only AFTER you have saved for them. Do not delude yourself that budgeting for an item is the same as saving for the item. Wait until the budget has become factual reality and the cash is in your pocket.
Recognize that spending money does not make you happier. This is because the incremental things you buy will have a lower marginally value to you. Spending quickly becomes a habit you cannot live without. Within months, your higher lifestyle will seem 'necessary' for your happiness. You will continue to aspire to 'more' and then 'more'. You raise the bar on your happiness when your lifestyle increases. Opinion polls ask "Are you having problems making ends meet?". The answers from rich people are the same as from the poor. Of course it is all in their heads. But that does not change their feelings. Before any purchase, ask yourself "Will this make me more happy?"
'Keeping up with the Jones' is a very real social pressure. And to move up the job rankings you must make contacts and socialize with people richer than yourself. They know perfectly well they earn more than you and will be quite willing to pick up the tab more often. Let them - with good grace. But keep your personal life under control. Keep up your friendships with poorer friends and don't delude yourself that richer friends are 'better' people.
Sweat the small stuff. Yes big purchases make more of a dent, but that is not the point. Being thrifty is a state of mind. If you sweat the small stuff you will be primed for good decisions on large expenses. A large retail industry segment has grown up catering to "affordable luxuries". Think Coach handbags, or power toothbrushes, etc. Each item, by itself is not material. But once you think 'you deserve it' for one item, you will treat all those small items similarly. The small stuff adds up. And then when faced with the choice between a stainless steel fridge and a black one for half the price, guess which one you are primed to choose.
Pick your life partner with care to their use and abuse of money. That may sound cold, but reality should trump lust. It is hard to sustain romance when your partner blows 'your' savings on a muscle car. What seemed like a cute 'princess' attitude before marriage, loses its charm when you realize she demands ONLY the best.
New research is showing that how you 'think about' saving changes your actual savings. North Americans are socially conditioned to see life as a linear event, and savings as the means to a better retirement. The future is seen as determined by past and present events. The problem is that optimistic beliefs that the future will be better than the present creates more optimistic assessments about future savings. Individuals defer savings as a result. Tam and Dholakia (2013) found that savings increased when they were presented as cyclical and routinized. The future will be exactly like the present so just focus on today's saving. So despite the warnings about the "pay yourself first" strategy above, it may be the optimal strategy.
Social norms are negatively impacting our wealth. Alarming 2013 research on US marriage preferences showed that
* Men prefer wives who earn less than themselves.
* Marriage rates decline when the predicted probability increases that a woman earns more than a man.
* Wives with the potential to earn more than their husbands participate less in the workforce.
* If the higher-earning wife does work, the gap between her realized and potential income is higher than for lower-earning wives.
* Wives who earn more than their husbands do more of the housework than wives earning less.
* Dissatisfaction with the marriage, and divorce rates increase when the wife earns more.
These findings show we are shooting ourselves in the foot financially for the sake of mistaken ego (men) and for the sake of pointless male approval (women).
All these products are considered safe. The rate of return ( % interest ) is stated at the start and guaranteed. The repayment of principal is guaranteed and happens at a specified time. The government guarantees the principal (Canada's Deposit Insurance Corp CDIC and US's Federal Deposit Insurance Corp FDIC), up to one million dollars. The downside is that the rates of return will be low. Eventually you will be willing to assume more risk. The most common progression is into real estate investments. But start here:
- Pay down debt. Paying off existing debt has great advantages.
- It corrects any misconceptions about how much money you have 'saved'. Savings is what is left after you have paid for all your purchases. Just because you have a 'savings fund' does not make that true savings when you also carry credit card debt.
- The return you get from paying off debt is higher than anything else available. There is always a spread between the interest rates you can earn on cash and the higher rates that you will pay to borrow. You take that spread for yourself when you invest in your own debt.
- It has no risk because income is certain.
- When evaluating whether debt is appropriate when you also have 'savings' you should make it satisfy two criteria. First, the interest rate on the debt must be lower than the rate of return you are realizing on the safest, lowest return asset own. Second, you should consider the debt to have financed the most risky asset you own. Ask whether you should be leveraging an asset of that risk.
- The income is not taxed, whereas other income will be. To calculate the after-tax rate of return, divide the debt's percent by (1-t), where t= your marginal tax rate. E.g. If the debt is costing you 8% and your tax rate is 30%, the 'investment return' from paying down the debt equals 8%/(1-.3)= 11.4% return from a regular investment.
- Warning. If the source of your funds is only temporary, i.e. you will have to re-borrow, this strategy may not work. Predict what interest rates you will be paying on the new debt. If it will be higher than your current terms, maybe it is better to leave things alone. Also consider any fees to close the debt and reopen a new line (transaction costs).
- Prepay expenses. We all face ongoing living expenses. Some repetitive types can be pre-paid at a discount. The discount is your interest income. For example, some property and auto insurance allows for monthly remittances. But these 12 payments total more than the annual cost. Make the single payment and keep the difference as income. E.g. Your landlord expects your cheque each month, but will not object to receiving a full years' payments up front. Arrange a discount that is agreeable to both of you. This calculation using a financial calculator is shown in Problem #1.
- Bank savings account. Far back in time the bank's savings account offered real interest rates. Now the rates are so low and the charges so high there is really no point to their use. Except for stock-piling 'cash-on-demand'. For that purpose a chequeing account will probably be cheaper. Your objective is to limit the charges you pay. Forget about maximizing the interest you earn.
- High interest savings accounts from brokerages and electronic banks and credit unions. This site from Red Flag compares the Canadian alternatives. This site from the Globe lists the posted rates.
- Canada Savings Bonds (CSB) and Canada Premium Bonds bought through your bank or directly from the government. There are no service charges. Premium bonds pay higher returns because they are only redeemable at year end, while the Savings bond is redeemable any time. The interest rate will change every year, but because both are redeemable at that time this creates no risk. You just have to make sure that you keep informed and do not allow your investment to continue at an unattractive rate simply because of laziness.
- Money Market (MM) Funds can be bought from your discount broker. They pool people's money like a mutual fund and buy short-term government T-bills and corporate paper. The broker will claim the rate quoted is guaranteed, but in reality the fund's value is determined by the market, which can change.
It was these products that provided the first evidence of the ensuing credit crunch that rocked the world in 2008. For the first time, these products experienced losses. They 'broke the buck'. Issuers had always sold them with an implict guarantee of principal safety, and so .... enter the lawyers.
- T-bills are issued by both US and Canadian governments. They have 30, 60, 90 day, etc. maturities. Most discount brokerages will effectively refuse to sell them. Instead you get a hard sell on their MM fund. The market yields of T-bills are published but those only apply to the very large purchases that are normal in their market.
- Annuities are bought from insurance companies. These products are bought when retired and drawing down savings. But behind their structure is a guaranteed rate of return and a $100,000 (in Cda and US) government guaranteed execution. These are discussed at length on the Annuities page.
- Floating Rate Preferred Shares are bought through your stock broker. They are listed like normal stocks on the exchange. Although your principal is not guaranteed, in reality any issues from a large, stable corporation will have little risk. Beware, though that in times of great stress, like the 2008 credit crunch, these shares' value fell 50% - more than normal preferred shares fell. All of a sudden, investors started considering the repayment risk that they normally ignore.
Like any preferred share, you need to read the prospectus before you buy. The return are usually paid monthly and are determined as some percent of the corporate Bank Prime rate. As Prime changes so does your return, so the price of the shares stays steady. BCE has a long list of these type of shares outstanding (e.g. Y and E). The price you pay for the stock between distributions will include the accrued return for the interim period, so watch the date of Record.
- Traditional Term Deposits, Certificates of Deposit (CD), Guaranteed Investment Certificates (GIC). These products are sold not bought. That means banks do not give you the information to make your own decision. They purposely have no documentation (or even list of rates) when you walk in the bank. They force you to wait for 'personal service' in a separate room that you cannot leave without feeling obliged to buy something. They make the options confusing and non-comparable so that you disclose your requirements, and let them chose for you. Do not allow this to happen. Print the full listing of possible options and rates from the web, make your decision, and take it with you. Or go through a broker such as Finizi.
- You first decide the minimum length of time before you will need the cash. The longer you can commit, the higher the rate offered because it allows them to 'do something' with your money. Ultimately your money is used either by governments to provide services, or by business to operate/expand. When your repayment is hanging over their heads, they cannot commit the money to projects that take time to realize.
Don't be tempted to buy a longer-term product just because it allows you to cash in early. There will always be a penalty for cashing in early. Probably, the products' %rates increase each year. This penalizes people who withdraw their money early, even though it is 'allowed'. When there is a chance you will need the money early, buy the product with that earlier maturity. Don't take the risk.
- Next you decide whether you want the interest to be paid out to you or reinvested (regular interest vs. compound interest). These terms are not really correctly used, but who cares as long as you understand their meaning. Which is better for you is a personal decision. A retired person may appreciate the regular cash. A young person with no immediate needs for cash may prefer the reinvesting option because it gets rid of reinvestment risk. Generally, the banks pay lower interest rates when monthly cash is paid out. But in economic terms there is no benefit, so don't forgo a higher return just because you think "it would be nice to have the cash".
If they do not specify, ask what rate the reinvested interest will earn. For most flat rate products the rate will be the same as the original product's rate. But with escalating rate GICs the interest reinvested will earn something different - possibly the going rate for a 1-year GIC at that later date. The math for dealing with these differences is shown below. You have to make an assumption about an unknown.
- If you decide you want the interest paid out, you then choose between monthly or yearly payments. Because 'a dollar today is worth more than a dollar tomorrow', you would expect a lower rate (these are quoted using simple interest) for the GIC paying more frequently. The lower rate is offset by the added income you can earn from reinvesting the interest faster. So its true 'economic' value would be the same as a higher interest yearly-pay GIC. In order to compare the different quoted rates you must convert them to the 'true' annual rate. See Problem #11.
But the rate the banks offer is always LOWER than that smaller return, so do not chose a payment option that is more frequent than what you absolutely must have. The worst abuse of this situation is found in 'compound interest' products that allow you to chose a more frequent compounding at the penalizing rate. Since the interest is not paid out there is no benefit from the more frequent 'payments'.
- Escalating rate GIC's increase the rate of interest each year. This is ingenious marketing.
- Buyers who show concern about inflation can be sold this product as 'inflation protection' with the claim that the increase in rates compensates for inflation.. This is not true. All debt instruments already incorporate expected future inflation in their rate. The risk remaining is the difference between the expected inflation and what actually happens. This product does not assume that risk. The yearly rates are pre-set when you buy the product.
- Buyers will be comparing rates between different banks/trusts. 99% of all buyers will not know the basic math to compare products because each offers a different set of rates.
- Buyers can be sold products with a longer time frame than they can safely commit to because early withdrawal is allowed. The large penalty for that early withdrawal results from foregoing the large rate of return you only get in the last year. In fact the banks will be hoping that you DO withdraw early.
- The issuer makes no commitment regarding the rate that will be earned by reinvested interest. They are completely offloading the reinvestment risk onto the buyer. They know that no buyer will realize this or take it into account. They need not offer higher rates even while they reduce their own risk.
MATH FOR COMPARING ESCALATING RATE GIC'S
Here is how to compare two escalating rate GIC's.
- Both have $1,000 invested for 3-years with compound interest (reinvested).
- (A) pays a flat, compounding rate = 5%.
- (B) pays a rising rate at: 4%, 4.5%, 6%.
You make the assumption you can reinvest interest at 4.75%.
Note that you should not assume the same rate as in (A) because you are assuming the risk that rates fall in the interim.
Your objective is to calculate the 'future value' of your investment in each case. How much money will you have at the end of the period? The calculation for product (A) can be simplified by the math
|A||Year||Interest earned in year||Principal at end of year|
|1||1,000 * 5 % = 50 ||1,000 + 50 = 1,050|
|2||1,050 * 5 % = 52.50 ||1,050 + 52.50 = 1,102.50|
|3||1,102.50 * 5 % = 55.13||1,102.50 + 55.13 = 1,157.63|
|B ||Year||Interest earned in year||Interest earned on reinvested interest||Principal at end of year|
|1 ||1,000 * 4 % = 40 || ||1,000 + 40 = 1,040|
|2 ||1,000 * 4.5 % = 45||40 * 4.75 % = 1.90 ||1,040 + 45 + 1.90 = 1,086.90|
|3 ||1,000 * 6 % = 60 ||(40 + 45 + 1.90) * 4.75 % = 4.13 ||1,086.90 + 60 + 4.13 = 1,151.03|
The conclusion is that product A has the higher return, but only slightly. It leaves you with $1,157.63, while (B) leaves you with $1,151.03. Be aware that product (B) exposes you to reinvestment risk - it is not for sure that you will be reinvesting the income at 4.75%. Rates may fall and you could get less.
If you want to determine the true annual rate of return, so that you can compare to other products use the procedure at Problem #6. Using inputs of PV=$1,000, n=3years, FV=$1,151.03 gives you the result i% = 4.8%.