쉐도잉 연습: Rates and Returns – Module 1 – Quantitative Methods – CFA® Level I 2026 - 영상으로 영어 말하기 배우기

Hey everyone, welcome to today's session.

We're going to dig into some really important stuff for the CFA Level 1 exam, interest rates and returns.

I know this topic can feel a bit like drinking from a fire hose, but hang tight.

We'll take it step by step.

By the end of this lecture, you'll have a solid handle on these concepts and know how to use them in real world scenarios.

Let's get rolling.

First off, let's chat about the time value of money, TVM.

This concept is a big deal in finance and investing.

Basically, the time value of money means that a dollar today is worth more than a dollar tomorrow.

Why is that?

Because you can invest that dollar today and earn some returns.

This principle helps us compare cash flows that happen at different times.

Imagine you have $9,524 today and someone offers you $10,000 a year from now.

The difference of $476 is the payoff for waiting a year.

This translates to an interest rate of 5%.

Interest rates can be broken down in three main ways.

Number one is required rate of return.

This is the minimum return that an investor expects to earn from an investment.

Think of it as the hurdle you need to clear to make the investment worthwhile.

Number two is discount rate.

This rate is used to bring future cash flows back to their present value.

It's like asking, what's that $10,000 next year worth in today's dollars?

Number three is opportunity cost.

This is the return you miss out on by choosing to spend money today rather than saving or investing it.

For example, if you spend $1,000 today, instead of investing it at a 5% return, you miss out on $1.50 of earnings.

Interest rates are made up of several components.

Number one is the real risk-free interest rate.

This is the return on a risk-free investment with no expected inflation.

Number two is the inflation premium, compensation for the loss of purchasing power due to inflation.

Number three is the default risk premium, compensation for the risk that the borrower might default.

Number four is the liquidity premium, compensation for the hassle of selling the asset without taking a hit on the price.

Number five is the maturity premium, compensation for the risk associated with holding a long-term investment.

So, these five components all come together to form the total interest rate.

Each piece reflects a different aspect of the risk and compensations involved in investing.

Now, let's dive deeper into each component.

Real risk-free interest rate.

Think of the safest investment out there, like a U.S.

Treasury bill with no expected inflation.

The return you get is the real risk-free rate.

It represents pure compensation for waiting.

Number two is the inflation premium.

Prices usually go up over time, right?

If you're lending money, you'll want compensation for the loss of purchasing power, which is where the inflation premium comes in.

For instance, if inflation is expected to be 2%, you'll want at least 2% added to your interest rate to keep your purchasing power intact.

number three is the default risk premium not all borrowers are

created equal lending to a startup is riskier than lending to

the government the default risk premium makes up for the chance

that the borrower might not repay the loan number four is the liquidity premium

if you need to sell your investment quickly you might have

to take a lower price this premium makes up for the difficulty of selling an asset without taking a big loss.

Think about selling real estate fast versus selling stocks.

Number five is the maturity premium.

Long-term investments carry more risk

because the future is uncertain the maturity premium Compensates for this

added risk a 30-year bond typically offers a higher yield than a five-year bond to make up for the increased risk

Next up, let's dig into the various rates of return

Knowing how to measure and interpret returns is key to making smart investment decisions There are two main types of returns.

One is the periodic income.

This includes cash dividends or interest payments you get from your investments.

Second is the capital gains or losses.

These come from changes in the price of your investments.

To measure return, we use different methods.

Let's start with the holding period return.

holding period return equals the price at the end plus the income minus the price at the beginning

all divided by the price at the beginning say you bought a stock for $100 received $5 in dividends

and sold it for $110 your HPR would be 15% next is the arithmetic mean return arithmetic mean return

equals the sum of returns for each period divided by the number of periods.

For example, if your returns over three years were 10%,

12%, and 8%, the arithmetic mean return would be 10% using this formula.

Now the geometric mean return.

This measures the compound annual growth rate of your investment.

geometric mean return equals the product of 1 plus the return in each period

raised to the power of 1 divided by the number of periods minus 1

if you had the same returns of 10 percent 12 percent

and 8 percent over three years the geometric mean return would be approximately 9.97 percent here's where gets interesting.

The geometric mean is usually lower than the arithmetic mean because it factors in the effects of compounding.

Let me give you an example to make this clear.

Imagine you have an investment that gains 50% one year and loses 50% the next.

If you look at the arithmetic mean, you might think, great, my average return is zero, so I haven't lost anything.

But let's dig deeper.

Suppose you start with $100.

A 50% gain in the first year boosts your investment to $150.

But a 50% loss in the second year cuts it down to $1.75.

So even though the arithmetic mean is zero, you've actually lost money.

This is because the geometric mean considers how each period's return compounds, reflecting the real growth rate over time.

To recap, the arithmetic mean simply adds up your returns and divides by the number of periods,

while the geometric mean takes into account how those returns compound over time.

That's why the geometric mean often gives a more accurate picture of your investment's performance, especially when returns are volatile.

And finally, the harmonic mean.

The harmonic mean is useful when dealing with averages of ratios, like prices per share.

It gives more weight to lower values and is used when averaging rates over time or across different categories.

For instance, if you're averaging travel speeds over a distance, the harmonic mean gives a more accurate measure than the arithmetic mean.

If you travel the first half at 30 miles per hour and the second half at 60 miles per hour,

the harmonic mean is a better reflection of your average speed.

Alright, let's quickly go over some key concepts related to cost averaging and some other types of means.

Cost averaging is an investment strategy where you invest a fixed amount of money periodically.

The idea here is to average out the cost of purchasing shares over time.

Imagine you're saving for your dream vacation.

Instead of putting a lump sum aside, you decide to invest a fixed amount, say $1.100 every month.

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This is the essence of cost averaging.

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Now, the stock market can be a roller coaster.

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By investing regularly, you buy more shares when prices are low and fewer when they're high.

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This helps to average out the cost per share you pay over time, potentially reducing the overall impact of market fluctuations.

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The harmonic mean is particularly useful when averaging ratios.

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You apply these prices to a constant amount of money to get a variable number of shares.

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So far, we've discussed common means, but what about data sets with outliers?

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Extreme values that skew the average.

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Here, we can utilize techniques like the trimmed mean and the Windsorized mean.

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The trimmed mean simply excludes a small percentage of the highest and lowest values before calculating the average.

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This helps to lessen the influence of outliers.

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The Windsor Arised mean takes a different approach.

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It replaces the highest and lowest percentages of values with the closest non-outlier values,

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essentially capping the extreme ends of the data set before calculating the average.

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Let's move on to two important ways to measure return.

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Money-weighted return, abbreviated as MWR, and time-weighted return, abbreviated as TWR.

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Money-weighted return is a lot like the internal rate of return.

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It measures the compound growth rate of your investments, considering the timing and amount of cash flows.

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For the money-weighted return, similar to the IRR, the formula is the sum of the cash flows at time T

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divided by 1 plus the IRR raised to the power of T equals 0.

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For example, let's say you invested $100 at the beginning of the first year.

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An additional $950 at the beginning of the second year withdrew $350 at the end of the second year

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and the balance at the end of the third year was $1,270.

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Plug these values into the formula and you solve for IRR, which tells you the rate at which the present value of these cash flows equals zero.

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This method is sensitive to the timing of cash flows.

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If you invest more money before a period of high returns, your MWR will be higher.

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Time-weighted return, on the other hand, measures the rate of return earned by a portfolio manager independent of cash flows.

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It's useful for comparing the performance of managers who don't control cash inflows or outflows.

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First, you need to determine the value of your portfolio just before any significant cash inflows or outflows.

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This gives you a baseline to work from.

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Next, calculate the holding period return for each sub-period.

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Each time there's a significant cash flow, you end one sub-period and start another.

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For each sub-period, use the holding period return formula we discussed earlier.

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Finally, you geometrically link the sub-period returns to find the overall time-weighted return.

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This means multiplying the returns of each sub-period together and then adjusting for the number of sub-periods.

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The formula looks like this

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For example if you had returns of 5% 10% and minus 3% over three periods the TWR would be approximately 3.86%

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TWR is great for evaluating portfolio managers because it strips out the effects of cash flows

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Letting you see the managers true performance

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Now let's talk about how to annualize returns and get a handle on continuously compounded returns

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Annualized return helps you compare returns over different time period by converting them into an annual figure

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Annualized return equals one plus the periodic return raised to the

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power of the number of periods in a year minus one for instance

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if you have a monthly return of one percent the annualized

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return would be approximately twelve point six eight percent annualizing returns

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lets you compare investments with different time horizons on the same

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scale comparing a monthly return to an annual return directly isn't useful

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but converting the monthly return to an annualized figure makes it

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comparable continuously compounded returns are used for modeling returns over continuous periods this method assumes

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that returns are being compounded at every possible instant continuously compounded

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return equals the natural logarithm of the price at the end divided by the price at the beginning.

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For example, if the price of a stock goes from $100 to $105,

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the continuously compounded return would be nearly 4.88%.

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Continuous compounding is a more accurate way to model returns in theory.

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It's especially useful in certain financial models and pricing derivatives.

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Let's briefly touch on some other important return measures gross return this is the return after deducting trading expenses

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but before management fees it shows the investments performance before considering management costs

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now moving on to net return

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this is the return after all expenses including management fees

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it reflects the actual return to the investor think of it as the amount you actually get to keep Next,

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let's talk about pre-tax and after-tax returns.

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These adjust for the impact of taxes on investment returns.

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Taxes can really cut into your net returns, so understanding pre-tax and after-tax returns is crucial for effective investment planning.

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Finally, we have real returns.

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These adjust for inflation, showing the true increase in purchasing power.

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Real returns are important for understanding how much you're actually gaining in terms of purchasing power.

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Alright folks, we're down to the final section of this learning module.

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Let's talk about leveraged returns.

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Leverage can really juice up both your gains and your losses.

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So it's a powerful tool that needs to be used wisely.

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You can achieve leverage in a couple of ways.

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One is futures contracts.

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This involves investing just a fraction of the asset's value, which can amplify your returns proportionally.

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It's like getting a bigger bang for your buck with less upfront cost.

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Now, moving on to number two is borrowing.

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This means using borrowed funds to invest.

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While this can significantly increase your potential returns, it also raises the stakes by increasing potential losses.

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Let me give you an example.

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If you invest $100 and borrow an additional $100 to invest,

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a 10% return on the investment results in a 20% return on your original $100.

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Sounds great, right?

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But here's the flip side.

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Leverage is a double-edged sword.

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It can magnify your gains, but it can also magnify your losses.

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If your investment drops by 10%, your loss will be 20% on the original amount when using leverage.

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So if things go south, they go south in a hurry.

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That's all for today's lecture.

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Understanding interest rates and returns is crucial for making smart investment decisions and doing well on the CFA exams.

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Remember to practice the examples and problems in your CFA curriculum to really nail down these concepts.

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Thanks for sticking with me and keep pushing forward on your journey to becoming a CFA charterholder.

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You have got this.

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