Pratica di Shadowing: Rates and Returns – Module 1 – Quantitative Methods – CFA® Level I 2026 - Impara a parlare inglese con i video

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.

100

This is the essence of cost averaging.

101

Now, the stock market can be a roller coaster.

102

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

103

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

104

The harmonic mean is particularly useful when averaging ratios.

105

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

106

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

107

Extreme values that skew the average.

108

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

109

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

110

This helps to lessen the influence of outliers.

111

The Windsor Arised mean takes a different approach.

112

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

113

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

114

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

115

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

116

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

117

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

118

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

119

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

120

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

121

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

122

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

123

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.

124

This method is sensitive to the timing of cash flows.

125

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

126

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

127

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

128

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

129

This gives you a baseline to work from.

130

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

131

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

132

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

133

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

134

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

135

The formula looks like this

136

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

137

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

138

Letting you see the managers true performance

139

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

140

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

141

Annualized return equals one plus the periodic return raised to the

142

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

143

if you have a monthly return of one percent the annualized

144

return would be approximately twelve point six eight percent annualizing returns

145

lets you compare investments with different time horizons on the same

146

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

147

but converting the monthly return to an annualized figure makes it

148

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

149

that returns are being compounded at every possible instant continuously compounded

150

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

151

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

152

the continuously compounded return would be nearly 4.88%.

153

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

154

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

155

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

156

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

157

now moving on to net return

158

this is the return after all expenses including management fees

159

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

160

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

161

These adjust for the impact of taxes on investment returns.

162

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

163

Finally, we have real returns.

164

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

165

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

166

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

167

Let's talk about leveraged returns.

168

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

169

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

170

You can achieve leverage in a couple of ways.

171

One is futures contracts.

172

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

173

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

174

Now, moving on to number two is borrowing.

175

This means using borrowed funds to invest.

176

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

177

Let me give you an example.

178

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

179

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

180

Sounds great, right?

181

But here's the flip side.

182

Leverage is a double-edged sword.

183

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

184

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

185

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

186

That's all for today's lecture.

187

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

188

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

189

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

190

You have got this.

✨ Video consigliato

506 frasi

Analyzing Statements of Cash Flows 1 (2025 CFA® Level I Exam – FSA – Learning Module 4)

Cambridge Exam PrepBusiness EnglishUniversity Students

134 frasi

What's all the Yellen About? Monetary Policy and the Federal Reserve: Crash Course Economics #10

IELTS PrepBusiness EnglishUniversity Students

55 frasi

Convergence and Divergence: The Return of Sequences and Series

Cambridge Exam PrepUniversity StudentsWorking Adults

311 frasi

Eco 155: Principles of Macroeconomics Class 1

IELTS PrepTOEFL PrepCambridge Exam Prep

185 frasi

Financial Assets versus Real Assets | Essentials of Investments | CFA exam | CPA Exam BAR

Cambridge Exam PrepBusiness EnglishUniversity Students

52 frasi

Vocabolario e note di pronuncia per questa lezione

Questo video contiene 190 frasi e 2337 parole da ripetere con lo shadowing. Il parlato dura 17:23. Chi parla mantiene un ritmo costante di circa 134 parole al minuto, comodo per lo shadowing. Solo il 81% delle parole rientra nelle 3.000 più comuni dell’inglese, quindi il lessico è impegnativo.

Vocaboli chiave di questo video

15 parole meno comuni del video, con pronuncia e significato:

invest /ɪnˈvɛst/ (verbo) — investire. To spend money, time, or energy on something, especially for some benefit or purpose; used with in.
compound /ˈkɑmpaʊnd/ (sostantivo) — composto, miscuglio. Anything made by combining several things.
inflation /ɪnˈfleɪ.ʃən/ (sostantivo) — inflazione. An act, instance of, or state of expansion or increase in size, especially by injection of a gas or liquid.
compensation /ˌkɑm.pənˈseɪ.ʃən/ (sostantivo) — compensazione. The act or principle of compensating.
geometric /ˌd͡ʒiː.əʊˈmɛt.ɹɪk/ (aggettivo) — geometrico. Of or relating to geometry.
divide /dɪˈvaɪd/ (verbo) — dividere, dividersi. To split or separate (something) into two or more parts.
compare /kəmˈpɛɚ/ (verbo) — paragonare. To assess the similarities and differences between two or more things [“to compare X with Y”]. Having made the comparison of X with Y, one might have found it…
formula /ˈfɔː.mjʊ.lə/ (sostantivo) — formula. Any mathematical rule expressed symbolically.
leverage /ˈlɛv.(ə.)ɹɪd͡ʒ/ (sostantivo) — potenza, leveraggio. A force compounded by means of a lever rotating around a pivot.
default /dɪˈfɔlt/ (sostantivo) — mora, morosità. The condition of failing to meet an obligation.
minus /ˈmaɪ.nəs/ — meno. Made less or reduced by (followed by an expression of number or quantity).
continuously /kənˈtɪnjuəsli/ (avverbio) — continuamente, costantemente. Without pause.
reflect /ɹɪˈflɛkt/ (verbo) — riflettere. To bend back (light, etc.) from a surface.
component /kəmˈpoʊ.nənt/ (sostantivo) — componente. A smaller, self-contained part of a larger entity. Often refers to a manufactured object that is part of a larger device.
portfolio /pɔːtˈfəʊ.liˌəʊ/ (sostantivo) — cartella. A case for carrying papers, drawings, photographs, maps and other flat documents.

I phrasal verb che sentirai

add up (verbo) — sommarsi. To take the sum of; to total.
deal with (verbo) — fare i conti. To handle verbally or in some form of artistic expression; to address or discuss as a subject.
hit on (verbo) — provarci con. To discover, pinpoint; to think up; to realize.
look at (verbo) — guardare. To observe or watch.

Pronuncia a cui fare attenzione

Chi parla usa 16 contrazioni e forme ridotte, come you're, you'll, we're. Pronunciale nella forma breve, così come le senti.

I suoni “th”: withdraw /wɪðˈdɹɔ/, worthwhile /ˌwɜː(ɹ)θˈwaɪl/, arithmetic /æɹɪθˈmɛtɪk/, logarithm /ˈlɑ.ɡə.ɹɪ.ð(ə)m/
I suoni “sh” e “zh”: inflation /ɪnˈfleɪ.ʃən/, compensation /ˌkɑm.pənˈseɪ.ʃən/, ratio /ˈɹeɪ.ʃoʊ/, crucial /ˈkɹuː.ʃəl/, essentially /ɪˈsɛnʃəli/
Parole lunghe — attenzione all’accento: compensation /ˌkɑm.pənˈseɪ.ʃən/, geometric /ˌd͡ʒiː.əʊˈmɛt.ɹɪk/, continuously /kənˈtɪnjuəsli/, portfolio /pɔːtˈfəʊ.liˌəʊ/, maturity /məˈtjʊəɹɪti/

Come esercitarsi con questo video

Ascolta tutto il video una volta senza parlare e annota le parole che non conosci.
Fai shadowing frase per frase a velocità normale, ripetendo ognuna finché il tuo ritmo coincide con quello di chi parla.
Registrati e confronta con l’originale, facendo attenzione a parole come invest, compound, inflation.

La grammatica di questo video

Le strutture che chi parla usa di più, con le parole esatte del video:

Struttura	Nel video
Frasi condizionali if + frase, will/would + verbo — una condizione e il suo risultato	If you're lending money, you'll want
Forma passiva be + participio passato — conta ciò che accade, non chi lo fa	can be broken · is required · are made
Present perfect have/has + participio passato — un’azione passata che conta ancora adesso	haven't lost · you've actually lost · we've discussed
Frasi relative who / which + frase — un’informazione in più su una persona o una cosa	power, which is · value, which can

Cos'è la tecnica dello Shadowing?

Shadowing è una tecnica di apprendimento delle lingue supportata da studi scientifici, originariamente sviluppata per la formazione dei traduttori professionisti e resa popolare dal poliglotta Dr. Alexander Arguelles. Il metodo è semplice ma potente: ascolti un audio in inglese di madrelingua e lo ripeti immediatamente ad alta voce — come un'ombra che segue il parlante con un ritardo di solo 1–2 secondi. A differenza dell'ascolto passivo o degli esercizi di grammatica, lo shadowing costringe il tuo cervello e i muscoli della bocca a elaborare e riprodurre simultaneamente i modelli di discorso reale. La ricerca dimostra che migliora significativamente la precisione della pronuncia, l'intonazione, il ritmo, il discorso connesso, la comprensione dell'ascolto e la fluidità del parlato — rendendolo uno dei metodi più efficaci per la preparazione alla prova di speaking dell'IELTS e per la comunicazione reale in inglese.

Tecnica dello shadowing: leggi la guida completa passo dopo passo →

Pratica di Shadowing: Rates and Returns – Module 1 – Quantitative Methods – CFA® Level I 2026 - Impara a parlare inglese con i video

Analyzing Statements of Cash Flows 1 (2025 CFA® Level I Exam – FSA – Learning Module 4)

What's all the Yellen About? Monetary Policy and the Federal Reserve: Crash Course Economics #10

Convergence and Divergence: The Return of Sequences and Series

Eco 155: Principles of Macroeconomics Class 1

Financial Assets versus Real Assets | Essentials of Investments | CFA exam | CPA Exam BAR

Risk Management: The Math Behind Profitable Trading | FTMO

Unit 1.1: Introduction to Business Management - IB Business Management

Derivatives: Crash Course Physics #2

Visa Transaction Processing: Visa Processing Fees and Interchange Rate Basics

FIN 1 Welcome to Finance!

Contemporary Topics 2 Unit 5 Lecture with Powerpoint

Untangling Signals of Market Stress