Crystal ball time - interest rates

JustAnotherSaver

mollycat said:

 the 2 subjects I was taught at school, Mathematics and Arithmetic.

I suppose we're from two different times. I'm not sure what they're taught today, whether it's the same as what i got or slightly different.

For our teaching - mathS was numbers. Division, multiplication, yada yada ... it's numbers so it was mathS. Algebra, geometry, pythagoras and all that jazz still involved numbers so it was mathS.

80s-90s.

And i'd go 2 year fixed with the lot

RG2015

JustAnotherSaver said:

mollycat said:

 the 2 subjects I was taught at school, Mathematics and Arithmetic.

I suppose we're from two different times. I'm not sure what they're taught today, whether it's the same as what i got or slightly different.

For our teaching - mathS was numbers. Division, multiplication, yada yada ... it's numbers so it was mathS. Algebra, geometry, pythagoras and all that jazz still involved numbers so it was mathS.

80s-90s.

And i'd go 2 year fixed with the lot

Banking involves numbers. Is that maths?

I can also think of a lot of other things that involve numbers but would not regard as maths.

AnotherJoe

Wow Mr Saver, yes you made a good point although of course taking a flyer on a few assumptions but i like the overall approach and i recall now something similar being done in Monevator which was aiming to replicate those "get at least 5% return from the stock market over X years" type of investments . 

I may end up doing a blended version of what you suggested, in that although I've now put the money in an Atom 1.5% 2 year account (for the record putting me £3k over the £85k limit  but something I'm happy to risk for simplicity)  i have other sources of cash and there's no reason i couldn't, say put another £20k into investments and then in three years time I'll be able to extract the £60k for sure along with something from the investments.

As someone pointed out some time ago, and it was a new word for me at the time, money is fungible, so its arbitrary where that £60k actually is. Maybe its the £65k in a deposit account in 3 years time or maybe its £45k from there and £20k from what was an initial £20k into investments and now is £30k. Or whatever.

And again, as an aside in 3 years I'll be giving this money to one of my kids for a house deposit, she isn't aware of that. For complex reasons outside the scope of here, she can't buy a house for 3 years.

If it was for me, I'd just be investing it all because I wouldn't have a three year clock ticking and I have enough cash. Again, first world problems, sorry.

RG2015

kinger101 said:

RG2015 said:

Algebra, geometry and arithmetic were not separated out and things like sets x,y graphs, vectors and binary numbers were added in. It drove my Dad mad "I don't know what it is but it's not Mathematics!"

There are 10 types of people.  Those that understand binary and those that don't.

The meaning of life. 101010

Mr.Saver

kinger101 said:

Mr.Saver said:

Personally I'm a risk taker. I'd construct the problem this way:
I have 60k to save or invest or do a little bit of both.
At the end of 3 years, I have to spend the 60k, and I get to keep anything left of it, be it the interest, dividends or capital gains.

Which means I need to guarantee that in the worst case scenario that I have 60k after 3 years, and I'd like to have a good chance to do better than a 3 years fixed term savings account. To achieve that, I will use a fixed rate savings account and a global developed world equities index tracker.

My assumptions are:
* Global developed world equities can lose up to 20% of their value in 3 years
* Global developed world equities has a median compound annual growth rate (CAGR) of 6.5% in 3 years
Reason: those are pessimistic estimations based on the past performance of global developed world equities in the last 50 years. In all rolling 3 years period over the last 50 years, global developed world equities GBP inflation adjusted returns have never been down by more than 17%, and the GBP inflation adjusted median CAGR is 6.9%.
* The AER of a 3 years fixed savings accounts is 1.55%
Reason: https://www.moneysavingexpert.com/savings/savings-accounts-best-interest/#fixedsavings
* There's no trading commissions, platform fees, fund management fees, transaction costs, taxes, etc. payable
Reason: this is purely for the sake of keeping it simple, and you should take fees and taxes into your consideration in the real world.

So, my goal is to have no less than 60k at the end of 3 years, and the return beats a 3 years fixed savings account in most cases (i.e. more than 50% of the time). The total return of a 3 years fixed savings account is easy to calculate, it's:
60k * ((1+1.55%)^3 - 1) = 2833.46

Now, instead of that, if I put the amount x in a global developed world equities index tracker, and the amount 60k - x in the savings account, and to ensure I have zero chance of have less than 60k at the end of 3 years, I'll need to assume the equities have only 80% of their value left. So the amount x can be found by solving this equation:
EDIT IN PROGRESS, the equations and calculations are incorrect!
(60k - x) * (1+1.55%)^3 + x * 80% = 60k
60k * (1+1.55%)^3 - x * (1+1.55%)^3 + x * 80% = 60k
60k * (1+1.55%)^3 - (x * (1+1.55%)^3 - x * 80%) = 60k
x * (1+1.55%)^3 - x * 80% = 60k * (1+1.55%)^3 - 60k
x * ((1+1.55%)^3 - 80%) = 60k * (1+1.55%)^3 - 60k
x = (60k * (1+1.55%)^3 - 60k) / ((1+1.55%)^3 - 80%)
x = 11461.12

If we put 11461.12 in global developed world equities, there's 50% chance we cloud make
11461.12 * ((1+6.5%)^3 - 1) = 2372.45
or more returns from the equities.

Because the rest of the money is saved in a fixed savings accounts, we are also guaranteed to earn
(60k - 11461.12) * ((1+1.55%)^3 - 1) = 2291.02
interest from the fixed savings account.

So in total we have 50% chance to make at least 4663.48. That is a lot better than the 2833.46 from only using the fixed savings accounts. But, what's the chance of this portfolio making less than 2833.46? Or, let me rephrase the question. What is the chance that the equities has a CAGR of 1.55% or less in 3 years? It's certainly in between 0% and 50%. Therefore, I will take my chances for the 50+% chance of making more than that, and knowing that I will have at least 60k left after 3 years. The other advantage of this? You get to use the PSA, dividends and CGT allowances, so it may be a bit more tax efficient for people who has unused dividends and/or CGT allowances.

The problem is your probabilities and growth rates are at best estimates based of historic values, and at worse, guesses.

As I said, the probabilities and growth rates are pessimistic estimations. They are based on the past global developed world equities performance since 1970.
Let's take one step back, and assume the next 3 years is much worse than any 3 consecutive years in last 50 years. If the market fall by 50% in the next 3 years, how much of a shortfall is that?
Note: for reference, the MSCI emerging market equities index, which is a lot more volatile than the developed world equities index, didn't even experience a 50% fall in any 3 consecutive years in the same 50 years time frame.
11461.12 * (50% - 20%) = 3438.34
If the OP managed to max out his ISA allowance and premium bonds, I'm sure he can find the 3.5k from elsewhere if the worst is to happen. Self-insure against the extremely unlikely and worse than worst case scenario is the cheapest way if it's planned for, and affordable.

Thrugelmir

Mr.Saver said:

* Global developed world equities has a median compound annual growth rate (CAGR) of 6.5% in 3 years
Reason: those are pessimistic estimations based on the past performance of global developed world equities in the last 50 years. In all rolling 3 years period over the last 50 years, global developed world equities GBP inflation adjusted returns have never been down by more than 17%, and the GBP inflation adjusted median CAGR is 6.9%.

Did you factor in exchange rates. Also that dividends for example are subject to withholding tax. Fifty years it wasn't possible to hold many overseas equities. Whether returns would be the same if capital exchange controls hadn't of existed who knows. 

AnotherJoe

RG2015 said:

kinger101 said:

RG2015 said:

Algebra, geometry and arithmetic were not separated out and things like sets x,y graphs, vectors and binary numbers were added in. It drove my Dad mad "I don't know what it is but it's not Mathematics!"

There are 10 types of people.  Those that understand binary and those that don't.

The meaning of life. 101010

2A in my world

Mr.Saver

Thrugelmir said:

Mr.Saver said:

* Global developed world equities has a median compound annual growth rate (CAGR) of 6.5% in 3 years
Reason: those are pessimistic estimations based on the past performance of global developed world equities in the last 50 years. In all rolling 3 years period over the last 50 years, global developed world equities GBP inflation adjusted returns have never been down by more than 17%, and the GBP inflation adjusted median CAGR is 6.9%.

Did you factor in exchange rates. Also that dividends for example are subject to withholding tax. Fifty years it wasn't possible to hold many overseas equities. Whether returns would be the same if capital exchange controls hadn't of existed who knows. 

Did you factor in exchange rates? Yes, the returns have taken GBP exchange rate and GBP inflation into consideration.
Also that dividends for example are subject to withholding tax. I ignored all fees and taxes in the post, so the withholding tax is not taken into consideration.
Whether returns would be the same if ... who knows. Well, no one knows. But does anyone know whether inflation would be higher than interest rate in the next 3 years?

kinger101

Mr.Saver said:

kinger101 said:

Mr.Saver said:

Personally I'm a risk taker. I'd construct the problem this way:
I have 60k to save or invest or do a little bit of both.
At the end of 3 years, I have to spend the 60k, and I get to keep anything left of it, be it the interest, dividends or capital gains.

Which means I need to guarantee that in the worst case scenario that I have 60k after 3 years, and I'd like to have a good chance to do better than a 3 years fixed term savings account. To achieve that, I will use a fixed rate savings account and a global developed world equities index tracker.

My assumptions are:
* Global developed world equities can lose up to 20% of their value in 3 years
* Global developed world equities has a median compound annual growth rate (CAGR) of 6.5% in 3 years
Reason: those are pessimistic estimations based on the past performance of global developed world equities in the last 50 years. In all rolling 3 years period over the last 50 years, global developed world equities GBP inflation adjusted returns have never been down by more than 17%, and the GBP inflation adjusted median CAGR is 6.9%.
* The AER of a 3 years fixed savings accounts is 1.55%
Reason: https://www.moneysavingexpert.com/savings/savings-accounts-best-interest/#fixedsavings
* There's no trading commissions, platform fees, fund management fees, transaction costs, taxes, etc. payable
Reason: this is purely for the sake of keeping it simple, and you should take fees and taxes into your consideration in the real world.

So, my goal is to have no less than 60k at the end of 3 years, and the return beats a 3 years fixed savings account in most cases (i.e. more than 50% of the time). The total return of a 3 years fixed savings account is easy to calculate, it's:
60k * ((1+1.55%)^3 - 1) = 2833.46

Now, instead of that, if I put the amount x in a global developed world equities index tracker, and the amount 60k - x in the savings account, and to ensure I have zero chance of have less than 60k at the end of 3 years, I'll need to assume the equities have only 80% of their value left. So the amount x can be found by solving this equation:
EDIT IN PROGRESS, the equations and calculations are incorrect!
(60k - x) * (1+1.55%)^3 + x * 80% = 60k
60k * (1+1.55%)^3 - x * (1+1.55%)^3 + x * 80% = 60k
60k * (1+1.55%)^3 - (x * (1+1.55%)^3 - x * 80%) = 60k
x * (1+1.55%)^3 - x * 80% = 60k * (1+1.55%)^3 - 60k
x * ((1+1.55%)^3 - 80%) = 60k * (1+1.55%)^3 - 60k
x = (60k * (1+1.55%)^3 - 60k) / ((1+1.55%)^3 - 80%)
x = 11461.12

If we put 11461.12 in global developed world equities, there's 50% chance we cloud make
11461.12 * ((1+6.5%)^3 - 1) = 2372.45
or more returns from the equities.

Because the rest of the money is saved in a fixed savings accounts, we are also guaranteed to earn
(60k - 11461.12) * ((1+1.55%)^3 - 1) = 2291.02
interest from the fixed savings account.

So in total we have 50% chance to make at least 4663.48. That is a lot better than the 2833.46 from only using the fixed savings accounts. But, what's the chance of this portfolio making less than 2833.46? Or, let me rephrase the question. What is the chance that the equities has a CAGR of 1.55% or less in 3 years? It's certainly in between 0% and 50%. Therefore, I will take my chances for the 50+% chance of making more than that, and knowing that I will have at least 60k left after 3 years. The other advantage of this? You get to use the PSA, dividends and CGT allowances, so it may be a bit more tax efficient for people who has unused dividends and/or CGT allowances.

The problem is your probabilities and growth rates are at best estimates based of historic values, and at worse, guesses.

As I said, the probabilities and growth rates are pessimistic estimations. They are based on the past global developed world equities performance since 1970.
Let's take one step back, and assume the next 3 years is much worse than any 3 consecutive years in last 50 years. If the market fall by 50% in the next 3 years, how much of a shortfall is that?
Note: for reference, the MSCI emerging market equities index, which is a lot more volatile than the developed world equities index, didn't even experience a 50% fall in any 3 consecutive years in the same 50 years time frame.
11461.12 * (50% - 20%) = 3438.34
If the OP managed to max out his ISA allowance and premium bonds, I'm sure he can find the 3.5k from elsewhere if the worst is to happen. Self-insure against the extremely unlikely and worse than worst case scenario is the cheapest way if it's planned for, and affordable.

I'd argue that any estimation based on a 50 year window isn't that pessimistic.  It's also not clear whether OP needs £60K absolute or £60K relative to today's values.  Your argument seems to be OP can afford to lose a little of it, which might be the case.  But you can't assess capacity for risk without knowing what OP is buying in 3 years, and how currency movements and inflation might impact its future price.  

Mr.Saver

kinger101 said:

Mr.Saver said:

kinger101 said:

Mr.Saver said:

Personally I'm a risk taker. I'd construct the problem this way:
I have 60k to save or invest or do a little bit of both.
At the end of 3 years, I have to spend the 60k, and I get to keep anything left of it, be it the interest, dividends or capital gains.

Which means I need to guarantee that in the worst case scenario that I have 60k after 3 years, and I'd like to have a good chance to do better than a 3 years fixed term savings account. To achieve that, I will use a fixed rate savings account and a global developed world equities index tracker.

My assumptions are:
* Global developed world equities can lose up to 20% of their value in 3 years
* Global developed world equities has a median compound annual growth rate (CAGR) of 6.5% in 3 years
Reason: those are pessimistic estimations based on the past performance of global developed world equities in the last 50 years. In all rolling 3 years period over the last 50 years, global developed world equities GBP inflation adjusted returns have never been down by more than 17%, and the GBP inflation adjusted median CAGR is 6.9%.
* The AER of a 3 years fixed savings accounts is 1.55%
Reason: https://www.moneysavingexpert.com/savings/savings-accounts-best-interest/#fixedsavings
* There's no trading commissions, platform fees, fund management fees, transaction costs, taxes, etc. payable
Reason: this is purely for the sake of keeping it simple, and you should take fees and taxes into your consideration in the real world.

So, my goal is to have no less than 60k at the end of 3 years, and the return beats a 3 years fixed savings account in most cases (i.e. more than 50% of the time). The total return of a 3 years fixed savings account is easy to calculate, it's:
60k * ((1+1.55%)^3 - 1) = 2833.46

Now, instead of that, if I put the amount x in a global developed world equities index tracker, and the amount 60k - x in the savings account, and to ensure I have zero chance of have less than 60k at the end of 3 years, I'll need to assume the equities have only 80% of their value left. So the amount x can be found by solving this equation:
EDIT IN PROGRESS, the equations and calculations are incorrect!
(60k - x) * (1+1.55%)^3 + x * 80% = 60k
60k * (1+1.55%)^3 - x * (1+1.55%)^3 + x * 80% = 60k
60k * (1+1.55%)^3 - (x * (1+1.55%)^3 - x * 80%) = 60k
x * (1+1.55%)^3 - x * 80% = 60k * (1+1.55%)^3 - 60k
x * ((1+1.55%)^3 - 80%) = 60k * (1+1.55%)^3 - 60k
x = (60k * (1+1.55%)^3 - 60k) / ((1+1.55%)^3 - 80%)
x = 11461.12

If we put 11461.12 in global developed world equities, there's 50% chance we cloud make
11461.12 * ((1+6.5%)^3 - 1) = 2372.45
or more returns from the equities.

Because the rest of the money is saved in a fixed savings accounts, we are also guaranteed to earn
(60k - 11461.12) * ((1+1.55%)^3 - 1) = 2291.02
interest from the fixed savings account.

So in total we have 50% chance to make at least 4663.48. That is a lot better than the 2833.46 from only using the fixed savings accounts. But, what's the chance of this portfolio making less than 2833.46? Or, let me rephrase the question. What is the chance that the equities has a CAGR of 1.55% or less in 3 years? It's certainly in between 0% and 50%. Therefore, I will take my chances for the 50+% chance of making more than that, and knowing that I will have at least 60k left after 3 years. The other advantage of this? You get to use the PSA, dividends and CGT allowances, so it may be a bit more tax efficient for people who has unused dividends and/or CGT allowances.

The problem is your probabilities and growth rates are at best estimates based of historic values, and at worse, guesses.

As I said, the probabilities and growth rates are pessimistic estimations. They are based on the past global developed world equities performance since 1970.
Let's take one step back, and assume the next 3 years is much worse than any 3 consecutive years in last 50 years. If the market fall by 50% in the next 3 years, how much of a shortfall is that?
Note: for reference, the MSCI emerging market equities index, which is a lot more volatile than the developed world equities index, didn't even experience a 50% fall in any 3 consecutive years in the same 50 years time frame.
11461.12 * (50% - 20%) = 3438.34
If the OP managed to max out his ISA allowance and premium bonds, I'm sure he can find the 3.5k from elsewhere if the worst is to happen. Self-insure against the extremely unlikely and worse than worst case scenario is the cheapest way if it's planned for, and affordable.

I'd argue that any estimation based on a 50 year window isn't that pessimistic.  It's also not clear whether OP needs £60K absolute or £60K relative to today's values.  Your argument seems to be OP can afford to lose a little of it, which might be the case.  But you can't assess capacity for risk without knowing what OP is buying in 3 years, and how currency movements and inflation might impact its future price.  

I'd argue that any estimation based on a 50 year window isn't that pessimistic.
In the last 50 years the world have seen bubbles and major crashes. The 50 years time contains many economic cycles. Using a longer time frame may not help improving the estimation, because the financial world 100 years ago is a lot different than today's. Even it does have some effects on the estimated numbers, it won't change the big direction. Equities over 3 years don't lose half of their value, and they outperform savings accounts most of the time.

It's also not clear whether OP needs £60K absolute or £60K relative to today's values.
If the OP needs today's 60k in 3 years, choosing a 1.55% interest rate savings account is unlikely to help either. Because the inflation in the last 10 years (2009-2019) averaged at about 3.1% per annual. (Source: https://www.bankofengland.co.uk/monetary-policy/inflation/inflation-calculator) In fact, by investing a part of the money in equities, the portfolio has a better chance to loss less buying power over time.

Your argument seems to be OP can afford to lose a little of it, which might be the case.
I didn't argue that the OP can afford to lose a little in the first post. In fact I've taken the market downturn into consideration and in the historically worst case scenario the OP would still have 60k at the end of 3 years. It was to answer your question that the estimation of 20% downturn may not be enough, I said that OP can afford to lose a little if the future turns out to be much much worse than the history.

But you can't assess capacity for risk without knowing what OP is buying in 3 years, and how currency movements and inflation might impact its future price.
What OP is buying in 3 years is irrelevant here, be it a deposit for a house in the UK or a fancy sport car imported from the EU, it has been budged for 60k in GBP. The budget should consider the currency movements, inflation and the future price, not the portfolio.