Assets portfolio combinations below this green line are what's called

the dominated assets.

So these are assets for a given level of volatility,

a given level of standard deviation.

There exist another combination, a small and

large stocks with the same standard deviation that gives a higher return.

Therefore, the original portfolio combination is dominated.

An example, in this case was 100% large stock portfolio.

100% large stock portfolio is close to this minimum variance,

that was 94% large, but a 100% large portfolio

as a standard deviation of 25% and an average return of 8%.

It turns out a portfolio that's 88% large, 12% small has

the same standard deviation at 25, but has an expected return of 8.8%.

So that would suggest, hey, a 100% large stock portfolio's

dominated if that same standard deviation and 88% large,

12% small portfolio gives you a higher return of 0.8 percentage points per year.

So dominated assets, you can refer to them as being inefficient.

A portfolio combination is inefficient., if there's another portfolio

that yields a higher average return with the same standard deviation.

So let's do a real world application of this and this is like the time to start

really paying attention, because this is the tip that could literally save you

thousands and thousands of dollars and you get it for free.

Now, what more could you want?

So literally, this could be a tip that could save you tens of thousands

of dollars by pointing out a real world potential dominated asset and

I brought this up in the first course in module one, worth repeating again.

So let's say, you have an S&P 500 index fund and

it has an annual expense ratio of 0.05%, 5 basis points per year.

There's another S&P 500 index fund.

Again, the S&P 500 is an index of 500 large US companies.

It has an annual expense ratio of 0.4%.

So, each of these mutual funds is following the S&P 500.

So there they have exact same thing,

except one has an expense ratio A 0.4% per year or 40 basis points.

The other 0.05% per year or five basis points.

And by the way, there are mutual funds out there with such low expense ratios for

index funds provided by major fund families.

And just for simplicity,

for the example, let's assume the S&P 500 has a 10% return per year.

So, what's the difference in the wealth that you accumulate by investing in these

two funds?

Funds A and funds B after ten years, after 20 years, after 40 years.

So what's the difference after 10 years and then after 20, after 40?

We did this example before, so no need to write it out again.

If we look at fund A,

it only has this expense ratio of five basis points per year.

So, we're compounding instead of at 10% at 9.95%.

So you aggregate that up a dollar investment after ten years after expenses

is $2.58 where for fund B, where the expense ratio is 0.4% per year.

So aggregated up by 9.6%, as opposed to 10%.

This $1 grows to $2.50.

So, you're 3.2% higher wealth by investing in fund A over fund B.

20 years, this difference is a factor of 6.6% higher wealth.

In fund A, then fund B after 40 years,

this is 1.136 is a ratio of fund A to fund B wealth.

So if you buy investing in fund A, you would have had 13.6% higher balance at

the end of 40 years and they are exactly the same.

They're both investing in the S&P 500 is fund A has a higher expense ratio.

So if your final balance would be a million dollars by investing in fund B,

you would have a million, $36,000 by investing in fund A.

So you may say, this 13.6 is a big deal or it's not a big deal.

But if you don't want the 136,000, you can feel free to send it to me.

I'll be happy to take it off your hands.

Let's consider another example and we'll be getting into examples like this or

talk about the difference between actively managed funds, and index funds later

in the course, and the evidence of the performance of actively managed funds.

So let's assume we have this fund A,

S&P 500 again with this annual expense of 0.05%,

only 5 basis points per year and such funds exist there out in the marketplace.

So now fund B,

instead of being an S&P 500 index fund is an actively managed large-cap fund.

It has annual expense of 1.25% per year.

So this is a mutual fund where the manager is trying to beat the market,

also picking among large stocks.

Therefore, this higher fee.

Maybe this was also purchased through a financial advisor or

broker, which may kind of add fees to the mix as well.

So therefore, we have this 1.25% assumed fee here.

Just an example.

Let's assume both the S&P 500 and

the large-cap fund have a 10% return each year.

So, I'm basically assuming the large-cap fund doesn't beat the S&P 500.

They each have the 10% return per year.

We'll get back to this.

This is a good assumption to make or

not when we talk about mutual funds in module four of this course.

Now, let's see the difference in wealth that emerges after 10 years,

20 years, 40 years.

And again, we did this example in the first course.

So no need to write it again, but

you can see here the differences are quite striking.

After ten years, fund A again, the $1.00 investment goes up to $2.58,

because we're compounding 9.95% per year as opposed to 10.

For fund B on the other hand with the 1.25% expense ratio,

we're now compounding at a return of 8.75%.

That only grows to $2.31.

Fund A has 11.6% wealth at the end of the day than

fund B in your account after a ten-year period.

Once you go to 20 years, the difference in the wealth,

if you have fund A versus fund B grossed almost 25% more if you used fund A.

After 40 years, your retirement account will have

55.1% more wealth in it using fund A, then fund B.

So, there's this wild factor here.

So this is something to take into account and

we'll hit this point again that remember,

expenses you pay are money from mutual funds or to kind of various advisors.

That's money that comes directly out of your pocket, so

you need to be sure you're getting some benefit from that.

In this case, we assume both funds give the same return.

This higher expense basically really reduces the return you

get from the fund and that just compounds over time

leading to these dramatic differences in wealth accumulation.

So now, let's summarize some key points from this video and

module one of my first investments course.

So over the last 80 years, the US stock market has

outperformed Treasury Bills by about 8% per year on average.

That's what we would call the equity market premium.

Also, small stocks have outperformed the overall market by a sizable margin.

Now, the interesting question is do we attribute that difference to small stocks

being riskier or does it just mean small stocks have historically been under-priced

and have been kind of a good investment?