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Rates and Returns – Module 1 – Quantitative Methods – CFA® Level I 2026 — Transcript

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0:00Hey everyone, welcome to today's
0:01session. We're going to dig into some
0:03really important stuff for the CFA level
0:06one exam, interest rates and returns.
0:10I know this topic can feel a bit like
0:12drinking from a fire hose, but hang
0:14tight. We'll take it step-by-step. By
0:17the end of this lecture, you'll have a
0:18solid handle on these concepts and know
0:21how to use them in real-world scenarios.
0:24Let's get rolling.
0:26First off, let's chat about the time
0:28value of money, TVM.
0:30This concept is a big deal in finance
0:33and investing. Basically, the time value
0:36of money means that a dollar today is
0:39worth more than a dollar tomorrow.
0:42Why is that?
0:43Because you can invest that dollar today
0:45and earn some returns. This principle
0:48helps us compare cash flows that happen
0:51at different times. Imagine you have
0:54$9,524
0:56today and someone offers you $10,000 a
0:59year from now.
1:01The difference of $476
1:03is the payoff for waiting a year.
1:06This translates to an interest rate of
1:085%. Interest rates can be broken down in
1:11three main ways. Number one is required
1:14rate of return.
1:16This is the minimum return that an
1:18investor expects to earn from an
1:20investment. Think of it as the hurdle
1:22you need to clear to make the investment
1:25worthwhile.
1:26Number two is discount rate. This rate
1:30is used to bring future cash flows back
1:32to their present value. It's like
1:34asking, "What's that $10,000 next year
1:37worth in today's dollars?"
1:39Number three is opportunity cost. This
1:42is the return you miss out on by
1:44choosing to spend money today rather
1:46than saving or investing it. For
1:48example, if you spend $1,000 today
1:51instead of investing it at a 5% return,
1:54you miss out on $1.50 of earnings.
1:59Interest rates are made up of several
2:01components. Number one is the real
2:04risk-free interest rate. This is the
2:06return on a risk-free investment with no
2:09expected inflation.
2:11Number two is the inflation premium,
2:13compensation for the loss of purchasing
2:15power due to inflation. Number three is
2:19the default risk premium,
2:21compensation for the risk that the
2:23borrower might default.
2:26Number four is the liquidity premium,
2:28oh, compensation for the hassle of
2:30selling the asset without taking a hit
2:33on the price.
2:37Number five is the maturity premium,
2:39compensation for the risk associated
2:41with holding a long-term investment.
2:44So, these five components all come
2:47together to form the total interest
2:49rate. Each piece reflects a different
2:51aspect of the risk and compensations
2:53involved in investing.
2:56Now, let's dive deeper into each
2:57component.
2:59Real risk-free interest rate.
3:01Think of the safest investment out
3:03there, like a US Treasury bill with no
3:05expected inflation.
3:07The return you get is the real risk-free
3:10rate. It represents pure compensation
3:13for waiting.
3:14Number two is the inflation premium.
3:17Prices usually go up over time, right?
3:19If you're lending money, you'll want
3:21compensation for the loss of purchasing
3:24power, which is where the inflation
3:25premium comes in.
3:27For instance, if inflation is expected
3:29to be 2%, you'll want at least 2% added
3:32to your interest rate to keep your
3:34purchasing power intact.
3:38Number three is the default risk
3:40premium.
3:41Not all borrowers are created equal.
3:44Lending to a startup is riskier than
3:47lending to the government. The default
3:49risk premium makes up for the chance
3:52that the borrower might not repay the
3:54loan.
3:55Number four is the liquidity premium.
3:59If you need to sell your investment
4:01quickly, you might have to take a lower
4:03price. This premium makes up for the
4:06difficulty of selling an asset without
4:08taking a big loss.
4:11Think about selling real estate fast
4:13versus selling stocks.
4:16Number five is the maturity premium.
4:20Long-term investments carry more risk
4:22because the future is uncertain. The
4:25maturity premium compensates for this
4:28added risk. A 30-year bond typically
4:31offers a higher yield than a 5-year bond
4:34to make up for the increased risk.
4:37Next up, let's dig into the various
4:39rates of return.
4:41Knowing how to measure and interpret
4:42returns is key to making smart
4:45investment decisions.
4:47There are two main types of returns. One
4:49is the periodic income.
4:52This includes cash dividends or interest
4:54payments you get from your investments.
4:57Second is the capital gains or losses.
5:00These come from changes in the price of
5:02your investments.
5:04To measure return, we use different
5:06methods.
5:07Let's start with the holding period
5:09return.
5:11Holding period return equals the price
5:14at the end plus the income minus the
5:17price at the beginning all divided by
5:20the price at the beginning.
5:22Say you bought a stock for $100,
5:25received $5 in dividends, and sold it
5:28for $110.
5:30Your HPR would be 15%.
5:33Next is the arithmetic mean return.
5:36Arithmetic mean return equals the sum of
5:39returns for each period divided by the
5:42number of periods.
5:43For example, if your returns over 3
5:45years were 10%, 12%, and 8%, the
5:50arithmetic mean return would be 10%
5:53using this formula.
5:55Now, the geometric mean return.
5:58This measures the compound annual growth
6:00rate of your investment.
6:03Geometric mean return equals the product
6:06of 1 plus the return in each period
6:09raised to the power of 1 divided by the
6:12number of periods minus 1.
6:16If you had the same returns of 10%, 12%,
6:19and 8% over 3 years, the geometric mean
6:23return would be approximately 9.97%.
6:28Here's where it gets interesting.
6:30The geometric mean is usually lower than
6:33the arithmetic mean because it factors
6:36in the effects of compounding. Let me
6:39give you an example to make this clear.
6:41Imagine you have an investment that
6:43gains 50% one year and loses 50% the
6:47next. If you look at the arithmetic
6:49mean, you might think, "Great, my
6:52average return is zero, so I haven't
6:54lost anything." But let's dig deeper.
6:56Suppose you start with $100. A 50% gain
7:01in the first year boosts your investment
7:03to $150.
7:05But a 50% loss in the second year cuts
7:08it down to $75.
7:11So, even though the arithmetic mean is
7:13zero, you've actually lost money.
7:16This is because the geometric mean
7:18considers how each period's return
7:20compounds, reflecting the real growth
7:23rate over time.
7:26To recap, the arithmetic mean simply
7:28adds up your returns and divides by the
7:30number of periods, while the geometric
7:33mean takes into account how those
7:35returns compound over time.
7:38That's why the geometric mean often
7:39gives a more accurate picture of your
7:42investments performance, especially when
7:44returns are volatile. And finally, the
7:47harmonic mean.
7:49The harmonic mean is useful when dealing
7:51with averages of ratios, like prices per
7:54share.
7:56It gives more weight to lower values and
7:58is used when averaging rates over time
8:00or across different categories.
8:03For instance, if you're averaging travel
8:05speeds over a distance, the harmonic
8:07mean gives a more accurate measure than
8:10the arithmetic mean.
8:12If you travel the first half at 30 mph
8:16and the second half at 60 mph, the
8:19harmonic mean is a better reflection of
8:21your average speed.
8:24All right, let's quickly go over some
8:25key concepts related to cost averaging
8:28and some other types of means.
8:30Cost averaging is an investment strategy
8:32where you invest a fixed amount of money
8:34periodically.
8:36The idea here is to average out the cost
8:38of purchasing shares over time. Imagine
8:42you're saving for your dream vacation.
8:44Instead of putting a lump sum aside, you
8:46decide to invest a fixed amount, say
8:49$100 every month.
8:52This is the essence of cost averaging.
8:54Now, the stock market can be a roller
8:56coaster. By investing regularly, you buy
8:59more shares when prices are low and
9:01fewer when they're high.
9:03This helps to average out the cost per
9:05share you pay over time, potentially
9:08reducing the overall impact of market
9:11fluctuations.
9:12The harmonic mean is particularly useful
9:15when averaging ratios. You apply these
9:17prices to a constant amount of money to
9:20get a variable number of shares. So far,
9:23we've discussed common means, but what
9:25about data sets with outliers? Extreme
9:27values that skew the average.
9:31Here, we can utilize techniques like the
9:33trimmed mean and the winsorized mean.
9:36The trimmed mean simply excludes a small
9:39percentage of the highest and lowest
9:41values before calculating the average.
9:45This helps to lessen the influence of
9:47outliers.
9:49The winsorized mean takes a different
9:52approach.
9:54It replaces the highest and lowest
9:56percentages of values with the closest
9:58non-outlier values, essentially capping
10:02the extreme ends of the data set before
10:05calculating the average.
10:08Let's move on to two important ways to
10:10measure return.
10:11Money weighted return, abbreviated as
10:14MWR, and time weighted return,
10:17abbreviated as TWR. Money weighted
10:20return is a lot like the internal rate
10:23of return.
10:24It measures the compound growth rate of
10:26your investments considering the timing
10:29and amount of cash flows.
10:31For the money weighted return, similar
10:33to the IRR, the formula is the sum of
10:37the cash flows at time T divided by 1
10:41plus the IRR raised to the power of T
10:44equals 0.
10:46For example, let's say you invested $100
10:49at the beginning of the first year,
10:51an additional $950 at the beginning of
10:53the second year, withdrew $350 at the
10:56end of the second year, and the balance
10:58at the end of the third year was $1,270.
11:04Plug these values into the formula and
11:06you solve for IRR, which tells you the
11:08rate at which the present value of these
11:10cash flows equals 0.
11:13This method is sensitive to the timing
11:16of cash flows. If you invest more money
11:19before a period of high returns, your
11:21MWR will be higher.
11:25Time weighted return, on the other hand,
11:27measures the rate of return earned by a
11:29portfolio manager independent of cash
11:32flows. It's useful for comparing
11:35the performance of managers who don't
11:37control cash inflows or outflows.
11:42First, you need to determine the value
11:44of your portfolio just before any
11:46significant cash inflows or outflows.
11:49This gives you a baseline to work from.
11:52Next, calculate the holding period
11:54return for each subperiod.
11:57Each time there's a significant cash
11:59flow, you end one subperiod and start
12:01another.
12:02For each subperiod, use the holding
12:04period return formula we discussed
12:06earlier.
12:08Finally, you geometrically link the
12:10subperiod returns to find the overall
12:12time-weighted return.
12:15This means multiplying the returns of
12:16each subperiod together and then
12:19adjusting for the number of subperiods.
12:22The formula looks like this.
12:25For example, if you had returns of 5%,
12:2710%, and minus 3% over three periods,
12:31the TWR would be approximately 3.86%.
12:37TWR is great for evaluating portfolio
12:40managers because it strips out the
12:42effects of cash flows, letting you see
12:45the manager's true performance.
12:49Now, let's talk about how to annualize
12:51returns and get a handle on continuously
12:54compounded returns.
12:56Annualized return helps you compare
12:58returns over different time period by
13:00converting them into an annual figure.
13:05Annualized return equals 1 plus the
13:07periodic return raised to the power of
13:10the number of periods in a year minus 1.
13:15For instance, if you have a monthly
13:16return of 1%, the annualized return
13:19would be approximately 12.68%.
13:24Annualizing returns lets you compare
13:26investments with different time horizons
13:29on the same scale.
13:31Comparing a monthly return to an annual
13:33return directly isn't useful, but
13:36converting the monthly return to an
13:38annualized figure makes it comparable.
13:41Continuously compounded returns are used
13:44for modeling returns over continuous
13:47periods. This method assumes that
13:50returns are being compounded at every
13:53possible instant.
13:55Continuously compounded return equals
13:58the natural logarithm of the price at
14:00the end divided by the price at the
14:03beginning.
14:04For example, if the price of a stock
14:06goes from $100 to $105,
14:10the continuously compounded return would
14:12be nearly 4.88%.
14:16Continuous compounding is a more
14:18accurate way to model returns in theory.
14:21It's especially useful in certain
14:23financial models and pricing
14:25derivatives.
14:27Let's briefly touch on some other
14:29important return measures. Gross return.
14:32This is the return after deducting
14:34trading expenses, but before management
14:36fees. It shows the investment's
14:38performance before considering
14:40management costs.
14:43Now, moving on to net return. This is
14:46the return after all expenses, including
14:48management fees. It reflects the actual
14:51return to the investor. Think of it as
14:53the amount you actually get to keep.
14:57Next, let's talk about pre-tax and
14:59after-tax returns. These adjust for the
15:02impact of taxes on investment returns.
15:05Taxes can really cut into your net
15:07returns, so understanding pre-tax and
15:10after-tax returns is crucial for
15:12effective investment planning.
15:16Finally, we have real returns. These
15:19adjust for inflation, showing the true
15:22increase in purchasing power.
15:25Real returns are important for
15:27understanding how much you're actually
15:28gaining in terms of purchasing power.
15:32All right, folks, we're down to the
15:34final section of this learning module.
15:36Let's talk about leveraged returns.
15:39Leverage can really juice up both your
15:41gains and your losses. So, it's a
15:43powerful tool that needs to be used
15:45wisely.
15:47You can achieve leverage in a couple of
15:48ways.
15:50One is futures contracts. This involves
15:53investing just a fraction of the asset's
15:55value, which can amplify your returns
15:58proportionally. It's like getting a
16:00bigger bang for your buck with less
16:03upfront cost.
16:05Now, moving on to number two is
16:07borrowing. This means using borrowed
16:09funds to invest. While this can
16:12significantly increase your potential
16:13returns, it also raises the stakes by
16:17increasing potential losses. Let me give
16:20you an example. If you invest $100 and
16:23borrow an additional $100 to invest, a
16:2610% return on the investment results in
16:29a 20% return on your original $100.
16:33Sounds great, right?
16:35But, here's the flip side. Leverage is a
16:37double-edged sword. It can magnify your
16:40gains, but it can also magnify your
16:43losses. If your investment drops by 10%,
16:47your loss will be 20% on the original
16:50amount when using leverage. So, if
16:53things go south, they go south in a
16:54hurry.
16:56That's all for today's lecture.
16:59Understanding interest rates and returns
17:01is crucial for making smart investment
17:04decisions and doing well on the CFA
17:07exams.
17:08Remember to practice the examples and
17:10problems in your CFA curriculum to
17:12really nail down these concepts. Thanks
17:16for sticking with me and keep pushing
17:17forward on your journey to becoming a
17:20CFA charter holder. You have got this.

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