In this workout, we're presented with a scenario of an investor who wishes to retire in 10 years time with the retirement portfolio of 2 million dollars.

And also hopes to purchase a holiday home in five years time at a price of 500,000.

There retirement portfolio is viewed as a necessity and the investor is only willing to accept a 5% probability of missing this goal.

But the holiday home is viewed more of as an aspiration.

And the investors willing to accept a 15% chance of not being able to fund this goal.

We're presented with some portfolios for the setup by a wealth management company.

And we're asked how much money the investor would need to invest to be able to meet these two goals.

We've got a scenario for a five-year time Horizon and also some data for a 10-year time Horizon as well for these four different investment portfolios.

For each different portfolio. We're given the expected or average return over the five-year time Horizon per year.

For also giving the standard deviation as our measure of risk.

And then in addition we're given the minimum return with an 85% probability. So this is the lowest return 85% of the time.

For each of the four different portfolios and then also the minimum return 95% of the time.

So if we go down to look at the retirement goal to begin with the amount of money that this investor wanted in their retirement portfolio on there retirement date was the two million dollars.

And we were told in the scenario that we have 10 years until that goal needs to be met.

If we try and identify now the optimum portfolio.

We need to look at the 10-year time Horizon.

And we also need to look at the 95% probability. Row. This investor is only willing to accept a 5% chance of not meeting their goal.

So if we look at the four portfolios, we can see that comparing these four different returns that are going to be the worst case outcome 95% of the time the best performing of these portfolios is portfolio a Which is expecting to generate 2.2% at least 95% of the time over a 10 year time Horizon. The return is quoted on a per annum basis.

portfolio a is the best one to go for and what we're expecting to return is 2.2% per year.

As a worst case outcome 95% of the time.

What the goals based investing approach now says is that if we want to have two million dollars in our portfolio in 10 years time with a 95% certainty. Well the level of return we're going to get at least 95% of the time is 2.2% So to identify how much money we need to invest in that portfolio today. We need to present value the money that we need in 10 years time.

at our 2.2% worst case return 95% of the time over the 10-year time Horizon and this tells us that we need 1 million 68,870.3 dollars today to invest in portfolio a which will grow to 2 million dollars at least at a 95% certainty.

If we then go down to the holiday home the holiday home had a expected purchase price of half a million dollars and we were looking to buy that holiday home in five years time. If we go back up to the five-year time Horizon table. We said that this investor is willing to accept a 15% probability of not meeting this goal. So we need to look at the minimum expected return within 85% probability Row for this five year time Horizon and if we compare all of these returns that we're going to get at least 85% of the time we can see that portfolio D is getting us the best return at least 85% of the time.

So this would be the portfolio that the investor should invest in for their holiday home goal.

Where they have slightly less need to meet that goal. They still want to meet with an 85% certainty but not as much as they're retirement portfolio.

So we're getting 4.2% return at least as our rate of return 85% of the time.

And if that is the case that we get 4.2% return per year at least 85% of the time then we can identify how much money we need to invest today in supportfolio B so that we have at least 500,000.

In five years time with an 85% level of certainty and to do that we take the 500,000 and Present Value it at our 4.2% over the course of five years to tell us that the amount of money that we need to invest today is 407,034.7 dollars so that if we earn that 4.2% return at least 85% of the time we will have at least half a million dollars.

85% of the time and therefore we can afford to buy that holiday home in five years time at least 85% of the time.

So in total this investor needs to invest the 1.6 million into portfolio a to allow them to achieve their retirement goal.

And then a further 407,000 into portfolio D to achieve their holiday home goal with the level of certainty that they have specified. So in total this investor would need 2 million 15,000,905 dollars to achieve both of these two goals.