The post Probability Concepts On CFA Level 1 appeared first on Financial Analyst Warrior.

]]>- Random variable: uncertain quantity/number
- Outcome: observed value of a random variable
- Event: single outcome or set of outcomes
- Mutually exclusive events: events that cannot occur at the same time
- Exhaustive events: list of events that includes all possible outcomes

If you roll a six-sided die, there are six possible outcomes, and each of these outcomes is equally likely. A six is as likely to come up as a three, and likewise for the other four sides of the die. What, then, is the probability that a one will come up?

Since there are six possible outcomes, the probability is 1/6. What is the probability that either a one or a six will come up? Given that all outcomes are equally likely, we can compute the probability of a one or a six using the formula:

In this case there are two favorable outcomes and six possible outcomes. So the probability of throw- ing either a one or six is 1/3. The above formula has many applications in the investment field and can also be applied to many games of chance.

For example, what is the probability that a card drawn at random from a deck of playing cards will be an ace? Since the deck has four aces, there are four favorable outcomes; since the deck has 52 cards, there are 52 possible outcomes. The probability is therefore 4/52 = 1/13.

If you know the probability of an event occurring, it is easy to compute the probability that the event does not occur. If P(A) is the probability of Event A, then 1 – P(A) is the probability that the event does not occur.

Events A and B are independent events if the probability of Event B occurring is the same whether or not event A occurs.

Let’s take a simple example. A fair coin is tossed two times. The probability that a head comes up on the second toss is 1/2 regardless of whether or not a head came up on the first toss. The two events are (1) first toss is a head and (2) second toss is a head. So these events are independent.

**Probability of A and B**

When two events are independent, the probability of both occurring is the product of the probabilities of the individual events. More formally, if events A and B are independent, then the probability of both A and B occurring is:

**P(A and B) = P(A) × P(B) **

Where:

- P(A and B) is the probability of events A and B both occurring
- P(A) is the probability of event A occurring
- P(B) is the probability of event B occurring

If you flip a coin twice, what is the probability that it will come up heads both times? Event A is that the coin comes up heads on the first flip and Event B is that the coin comes up heads on the second flip. Since both P(A) and P(B) equal 1/2, the probability that both events occur is:

**1/2 × 1/2 = 1/4**

If Events A and B are independent, the probability that either Event A or Event B occurs is:

**P(A or B) = P(A) + P(B) – P(A and B)**

In this discussion, when we say “A or B occurs” we include three possibilities:

- A occurs and B does not occur
- B occurs and A does not occur
- Both A and B occur

For example, if you flip a coin two times, what is the probability that you will get a head on the first flip or a head on the second flip (or both)? Letting Event A be a head on the first flip and Event B be a head on the second flip, then P(A) = 1/2, P(B) = 1/2, and P(A and B) = 1/4. Therefore,

**P(A or B) = 1/2 + 1/2 – 1/4 = 3/4.**

If you throw a six-sided die and then flip a coin, what is the probability that you will get either a 6 on the die or a head on the coin flip (or both)? Using the formula,

**P(6 or head) = P(6) + P(head) – P(6 and head) **

** = (1/6) + (1/2) – (1/6)(1/2)**

** = 7/12**

Often it is required to compute the probability of an event given that another event has occurred. For example, what is the probability that two cards drawn at random from a deck of playing cards will both be aces? It might seem that you could use the formula for the probability of two independent events and simply multiply 4/52 x 4/52 = 1/169. This would be incorrect, however, because the two events are not independent. If the first card drawn is an ace, then the probability that the second card is also an ace would be lower because there would only be three aces left in the deck.

Once the first card chosen is an ace, the probability that the second card chosen is also an ace is called the conditional probability of drawing an ace. In this case, the “condition” is that the first card is an ace. Symbolically, we write this as:

P(ace on second draw | an ace on the first draw)

The vertical bar “|” is read as “given,” so the above expression is short for: “The probability that an ace is drawn on the second draw given that an ace was drawn on the first draw.” What is this probability? Since after an ace is drawn on the first draw, there are 3 aces out of 51 total cards left. This means that the probability that one of these aces will be drawn is 3/51 = 1/17.

If Events A and B are not independent, then:

**P(A and B) = P(A) x P(B|A)**

Applying this to the problem of two aces, the probability of drawing two aces from a deck is:

**4/52 x 3/51 = 1/221**

Tree diagrams can be used to represent an investment problem with various probabilities of outcome:

This tree diagram illustrates the earnings per share of a firm given various economic scenarios. The total probabilities of outcomes should add up to 100% and the expected EPS is given by computing the weighted average of all the end scenarios’ EPS.

This formula is used to update probability given the addition of new information. The result is the up- dated probability of an event and is expressed as:

I hope you found this article on Probability Concepts On CFA Level 1 valuable. If you are currently studying for the upcoming Level 1 exam, I invite you to check out the CFA Level 1 Hacks that covers the most important aspects and concepts on the exam. If you have any questions, I invite you to contact us today.

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]]>The post Episode #11: What is Monte Carlo Simulation appeared first on Financial Analyst Warrior.

]]>On this episode, we cover Monte Carlo Simulation :

- What is Monte Carlo Simulation?
- How likely will the simulation be on the exam?
- Why it is important to understand the principal for the CFA Level 1 exam?
- Practical real life applications.
- Much more

If you are currently studying for the upcoming CFA© Level 1 exam, then we invite you to check out our CFA© Level 1 Study Hacks as well as the CFA© Level 1 Starter Kit that features 100 top mistakes CFA© candidates make on their CFA© Exam.

We hope you enjoy the show and we invite you to leave us feedback and contact us if you have any questions about Financial Analyst Warrior or the CFA® examination.

We invite you to connect with us on:

Facebook | Twitter |Google+

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]]>The post Monte Carlo Simulation in CFA Level 1 appeared first on Financial Analyst Warrior.

]]>Monte Carlo methods are used to handle both probabilistic and deterministic problems according to whether or not they are directly concerned with the behaviour and outcome of a random process. In the case of a probabilistic problem a simple Monte Carlo approach is to observe random numbers, chosen in such a way that they directly simulate the physical random processes of the original problem, and to infer the desired solution from the behaviour of these random numbers.

Monte Carlo simulation has wide application in performing risk analysis by building models of possible results by substituting a range of values (a probability distribution) for any factor that has inherent uncertainty( GDP growth, inflation rate, interest rate, asset performance…). It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete.

Monte Carlo simulation produces distributions of possible outcome values. By using probability distributions, variables can have different probabilities of different outcomes occurring. Probability distributions are a realistic way of describing uncertainty in variables of a risk analysis.

In corporate finance for example, a company may need to value a project, which may involve an initial outlay with future expected profits. If these future profits can be estimated accurately then the firm can determine whether these profits will outweigh the costs and can then decide whether to proceed with the project or not. The factors affecting the future profits could consist of many variables, including but not limited to interest rate fluctuations, currency exchange rate changes, macro-economic factors, labour costs, environmental issues or advancements in technology. Since each one of these factors can be multi-dimensional there could be a very large amount of parameters to be estimated, each having its own distribution. Therefore Monte Carlo simulation methods can be implemented.

As we will see in the derivatives section, stock options change in value depending on the price of an underlying stock, which itself can be affected by a very large number of factors. Simulation can be used to generate thousands of possible (but random) price paths in order to estimate the future value of an option. This can then allow a price to be assigned to the option at the current time point.

Yet another investment application is portfolio evaluation, which involves estimating the value of a collection of financial instruments such as stocks or bonds to determine the wealth to be gained. Monte Carlo methods can be used to simulate the correlated behaviour of the components of the portfolio over time in order to assess how the portfolio is affected by certain price level changes in order to estimate the value of the portfolio.

Monte Carlo methods provide flexibility and can handle multiple sources of uncertainty however the techniques are not always appropriate. In general such methods are likely to be preferable when there exist several sources of uncertainty such as in the above cases.

We hope you found this article on Monte Carlo simulation valuable. If you have any question about the CFA © Level 1 exam, we invite you to contact us. If you are preparing for the upcoming CFA © Level 1 exam, we invite you to purchase our CFA © Level 1 Bundle. Although you will not be required to use Monte Carlo simulation on the actual exam. It is still important that you understand the principle behind it.

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]]>The post Episode #10 | How to foster a Warrior mentality to help you study and prepare for the CFA Exam appeared first on Financial Analyst Warrior.

]]>If you are currently studying for the upcoming CFA© Level 1 exam, then we invite you to check out our CFA© Level 1 Study Hacks as well as the CFA© Level 1 Starter Kit that features 100 top mistakes CFA© candidates make on their CFA© Exam.

On this episode, we cover interesting real world questions :

- How to foster a Warrior mentality in order to help you concentrate and study for the upcoming CFA Level 1 exam
- Real world Capital Budgeting application from the CFA Level 1 exam
- Much more

We hope you enjoy the show and we invite you to leave us feedback and contact us if you have any questions about Financial Analyst Warrior or the CFA® examination.

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]]>The post Episode #9 | Robo Advisors, Future of Investment Advisors, Valuations models and much more appeared first on Financial Analyst Warrior.

]]>If you are currently studying for the upcoming CFA© Level 1 exam, then we invite you to check out our CFA© Level 1 Study Hacks as well as the CFA© Level 1 Starter Kit that features 100 top mistakes CFA© candidates make on their CFA© Exam.

On this episode, we cover interesting real world questions :

- What is an Robo Advisor and what it means for the future of Investment Advisors and CFA candidates
- Main valuation models, their applicabilities, relevances and the holistic approach to choosing investments
- Practical advice for future CFA charterholders
- Much more

We hope you enjoy the show and we invite you to leave us feedback and contact us if you have any questions about Financial Analyst Warrior or the CFA® examination.

We invite you to connect with us on:

Facebook | Twitter |Google+

Don’t forget to sign up to our newsletter below.

The post Episode #9 | Robo Advisors, Future of Investment Advisors, Valuations models and much more appeared first on Financial Analyst Warrior.

]]>The post How to Foster a Warrior Mentality Ahead of the CFA Exam appeared first on Financial Analyst Warrior.

]]>We have discussed in previous articles that the CFA exam challenges at least as much your mental and emotional fortitude than your knowledge of finance theory. The constant fight that is entailed in studying for a CFA charter is the reason we called this website Financial Analyst Warrior. This is a fight against many enemies, namely:

- Boredom
- Distractions
- Laziness
- Internet
- Social media
- Stress

The human response when facing a danger has been summarized by the three Fs: Flee, Freeze or Fight.

Although it would be a stretch to claim that studying for the CFA exam constitutes a “danger” we can all agree that it is a stressful process. Some will abandon their pursuit along the way (flee), some will be intimidated by the task and constantly postpone their study (freeze) and some will fight on!

The fighting analogy not only describes accurately the warrior mindset that allows us to aggressively pursue our goals, it also provides us with many lessons, learned on the battlefield (the real one) that can be applied to less belligerent tasks, such as studying for an exam.

The warrior image does convey a violent and aggressive vibe to a perfectly academic and intellectual pursuit which some could find curious. However, from my personal experience, this testosterone-injected image is not only the best way to succeed in an exam or competition; but also to accept the any outcome with grace and stoicism.

A good warrior is strong and impassive in the face of danger and doesn’t let his/her emotion get in the way of quick and efficient decision making. Great warrior exudes confidence and control without reeking of cockiness (actually I am sure most great warriors ranged between a bit cocky and humongous douchebags). We believe the warrior image incorporates the perfect mix of calm and aggression that is required to attack the exam while maintaining a discipline and methodical approach to nail all the questions.

We discussed the importance of a ritual in a previous article but its importance cannot be overplayed. The ritual can be seen as a form of meditation that lets your mind transition from whatever you were doing to the new task to tackle which can be studying for the CFA, undergoing a practice exam or writing the actual exam.

A ritual does not have to be an elaborate dance or a goat sacrifice as an offering to the Gods (although it is preferable). It can be as simple as a small routine where you prepare your body and soul for the upcoming task. Back in college, I would always listen to aggressive gangsta rap before an exam. That would put me in the zone and clear my mind off of any other concerns or distraction.

You do not need to be superstitious to perform a warrior ritual. The important thing is to provide you with a buffer between whatever you were doing before and the CFA related study/exam.

Visualization is the practice of playing a scenario in your hear before it happens. Athletes always visualize their upcoming competition in order to be ready for all scenarios and contingencies. Ahead of combat, warriors should also visualize their enemy and see them perish a thousand times. When I say visualization I don’t mean simply seeing yourself sitting down answering questions, that does not take much imagination.

Candidates need to visualize everything that will happen from the morning of the exam onward; how they will wake up, what they will eat, how they will get to the exam facility and enter into the exam room. When you visualize these mundane steps several times in your hand, you will be less prone to distraction and more focused when you actually go for the exam. Imagine going into a new city, you naturally look around because everything is new for you and your attention is all over the place trying to absorb as much information as possible. When you walk in your own neighborhood, you are not distracted by anything since you have been there several times. Your attention is therefore more focused toward whatever you are doing.

This is also the reason why it is always advisable to visit the exam location in advance. It is harder to visualize something you have never seen before…

It is said that Shaolin Kung-Fu was developed as a series of exercise that helped the Shaolin Buddhist Monks stay in shape despite long hours of meditation. The purpose was to maintain strong and healthy bodies to sustain endless sessions of sedentary meditation. These monks understood that it is easier to concentrate when the body has a regular opportunity to move around.

As a rather fidgety guy, I have always found that the most difficult part of the CFA is the requirement to spend long hours sitting in a chair looking at a textbook. Back in college, I barely studied so it was not that much of an issue. To nail the CFA, there is no getting around it, you need to put in a significant amount of hours. The only thing that saved me was that I would train in between study session so that my body was relatively tired and the “down time” provided by the studying was welcomed.

An example of how you can cultivate your body to withstand long hours of studying is by splitting your reading sessions with short workout sessions. Exercise can be as simple as a few push-ups, sit ups or jumps just to get the juices flowing. There are tons of short exercises that does not require any equipment or space (check Youtube). I suggest to place a special focus on back and shoulder exercise since these are the areas that suffer the most from being hunched over books for extend periods.

Discipline is an essential ingredient to succeed at most tasks in life yet it is very difficult to maintain for an extended period. First of all let clear out some misconception about discipline. It is not true that some people have it and some do not; everyone can have discipline if they are properly motivated. Also, discipline is never constant. I may keep to my study schedule for 2 month and then suddenly slack off. It is impossible to be always perfectly discipline but the warrior example gives us a perfect image to strive for.

In the military discipline is imposed from above so there is not many opportunities to deviate and if so there are harsh sanctions. When studying, there is no such authority that imposes a studying regimen and each candidate is left to their own regulations. There are no direct consequences from slacking on the studying since the fact that I forgo my curriculum readings today has arguably a small impact on the pass/fail result on the exam. Given this lack of accountability, some candidates find sources of discipline elsewhere. Some find it in the shame they will have to endure given a failure. Some find comfort in their salary bump once the exam passed. Candidates who already have competitive DNA will find motivation and discipline in the sheer fact that they defeated the dreaded CFA exam single-handedly.

If you have a hard time maintaining discipline when you are studying or trying to perform anything for that matter, try the following mind hack that I have been implementing for many years in various situations.

**Mind-hack to Discipline Yourself**

Whenever you feel like slacking off or watching TV/Internet or doing anything else than what you are supposed to do, imagine that you are being filmed. Imagine that there is a movie being filmed in secret about your life (similar that movie with Jim Carey) and that millions of people will be watching (or are watching live). If you can visualize that, the desire to look good and to give an image of yourself as a hard-working discipline cool guy or girl will usually be stronger than the appeal of laziness. This is a way to remain accountable even when you are alone. In this case you are accountable to millions of imaginary viewers that will potentially judge you and look down on you if you behave like a giant wuss. This is a form of self-imposed imaginary peer pressure and should obviously not be abused since that may lead some people to feel overly guilty and depressed all the time. For my part, thanks to this simple trick, I am usually able to be relatively discipline and look pretty cool even when I’m alone. ..

I read recently somewhere (although I cannot remember where) that fearlessness does not really exist. In reality, those who appear fearless, like warriors, are just better able to control their fears than the rest of us. It makes sense since it is hard to believe that someone who risks not only death but permanent injury and excruciating pain, does not shit his pants, warrior or not. Being able to stand up in the face of danger is not something everyone can accomplish instinctively. However, there are ways to build our fortitude so that we can avoid being overcome with fear.

One way is to visualize, embrace, study and even cherish the fear and its source. The soldier going to battle faces the distinct possibility of losing his life or a limb. He needs to understand that and consciously make effort that it does not happen. Some people do not like to envisage failure as an option. In my case I think you need to visualize the worst case scenario and see what would happen if this scenario does occur. This is a tip that I got from Tim Ferris in his 4-hour workweek book. According to him, most of the time, the worst-case scenario is not as bad as we think … although that certainly does not apply for the warrior since death is the worst-case scenario…

By visualizing and accepting the possibility of failure on the CFA exam, you can reach an inner peace and you may be able to face the exam with calm and impassiveness. Unfortunately, my best advice to overcome fear is failure itself although that is hardly an option in an exam scenario. Although you wouldn’t fail the exam just so that next time around you can be fearless, failure helps tremendously to de-dramatize the “worst-case-scenario”. I have experienced failure several times in all fields of life (school, CFA, business, career, sports, girls, pets, cooking, …) but every time (except with girls) it was a great learning experience and it allowed me to try again without being affected by the fear of failure.

If you don’t wish to fail the CFA just for the sake of becoming fearless (please don’t do that!), you can try building your resistance to fear by attempting any other activity that instills stress. For example if you are afraid of getting your ass kicked, try a mixed martial arts class. Or if you are afraid of heights, go skydiving. This will teach you to familiarize yourself with fear and possibly conquer it.

So far we talk about the pre-war ritual, the pre-war visualization, the physical preparedness, the discipline in your studies and the ability to conquer your fear. However, lets be honest, being a warrior is mostly about eradicating your enemy which requires aggression and combativeness. A soldier needs to keep on fighting despite the injuries and setbacks suffered. For a candidate, this translate into the resilience of answering question after question and not letting a bad streak affect them mentally. This may seem trivial but when you have to face a few questions in a row for which you did not know the answer beyond doubt, it can have a disastrous impact on the rest of your exam. You may enter into a spiral of self-doubt and candidates may get the impression that they are under-prepared for the exam. This is especially true in the level 2 exam where you have 6 consecutive questions on the same topic. If it happens to be your weak topic, your confidence level may drop quickly.

The first step in fighting the spiral of self-doubt is to be aware of it. Each question is a new fight and should be attacked head-on without other results affecting your mindset. Remember that if there are 180 questions and you typically require to get 70% of them correct to pass, that means you are allowed to answer incorrectly on 54 of those and still pass. Unless you get a streak of 54 tough questions, there is no reason for you to be affected by a bad streak.

I hope this helps you to visualize what we mean by adopting a warrior-like attitude. The main takeaway here is to not let the emotional factor squander the effort you spent in studying the material. Visualize yourself as a noble and powerful general going to war with the firm resolve to defeat the enemy….but just visualize it, do not talk about it or you will be seen as a total lunatic…

We also invite you to check out our latest CFA Level 1 Starter Kit.

We created this CFA Level 1 Starter Kit to help you better prepare for the upcoming CFA exam.

We want to help you maximize your study efficiency and avoid the most common mistakes candidates make on the CFA Level 1 exam.

- Top 100 Pitfalls (mistakes) to avoid on the CFA Level 1 exam (+50 pages PDF eBook)

- Exam Strategies (9 pages PDF article)
- Concentration Tips (9 page PDF article)
- 3 study schedules : 16 weeks, 14 weeks and 10 weeks study plans (customizable in Excel)

By using the resources found in this Study Kit, you will be able to better focus on your studies knowing that you will have enough time to cover everything before the exam. You will also the learn the most frequent errors CFA Level 1 Candidates make and how to avoid them on the exam day.

The post How to Foster a Warrior Mentality Ahead of the CFA Exam appeared first on Financial Analyst Warrior.

]]>The post When Asset Allocation becomes a commodity through a Robo Advisor, how can investment advisors adapt and stay relevant? appeared first on Financial Analyst Warrior.

]]>Its seems that every major industry that has stagnated over the past decades is currently undergoing tremendous disruption and transformation. Airbnb is disrupting the hospitality industry and Uber is disrupting the transportation and taxi industry. It now looks like its time for the financial industry to be disrupted with Robo Advisors. Financial professionals have always relied on the latest innovations in technology to get an advantage in the capital markets. For the last couple of years, we have seen this very technology turn full circle and begin to replace these very own professionals as well as eliminate redundancy and human errors. Flash trading and algorithms trading have redefined the roles of traditional stock traders. Now Robo Advisors are questioning the value of Investment Advisors and redefining the concept of asset allocation in the portfolio management industry.

In its simplistic form, Robo Advisors are computer programs that help investors allocate, invest and rebalance their portfolios automatically on an ongoing basis while charging management fees that are far lower compared to the traditional Investment Advisory industry. If we take the US as an example, the average retail Investment Advisor charges between 1% and 3% of assets under management to perform various tasks around structuring and occasionally rebalancing individual’s portfolios. The two leading Robo Advisory firms in the US WealthFront and Betterment charge as little as 0.25% on portfolios with assets over $10,000. Some firms such as WiseBanyan do not charge any fees at all on assets under management and instead rely on selling add-on services to generate revenue.

The underlying premise of a Robo Advisor is very simple. You pick an amount you want to invest. You pick your investment objectives and your risk profile and then computerized algorithms take over. As the markets evolve and your investment horizon advances, your capital is automatically allocated among specific trading instruments like ETFs. You can also set automatic investment plans where new capital is automatically taken from your bank account and invested in your constantly changing personal investment portfolio. Although this might sound like traditional funds of mutual funds, it is important to note that rebalancing in the fund of funds is done among the predefined funds, while Robo Advisors rebalance your portfolios based on changing markets conditions, different types of ETFs and your risk/reward preferences that can change throughout your investment horizon.

The Robo Advisort industry is fairly new. Much of its growth and popularity is attributed to two things. Technology and Fees. Millennials are highly adept at tech and spend more and more time on their mobile devices. WealthFront stated that over 90% of its clientele are under the age of 50 and over 60% of that category are under the age of 35. The dominant companies in the industry invest in their platforms, user experiences and transparency. With technology and user experience being at the centre of their services, Robo Advisory companies are able to better connect to their customers and facilitate the process of investing. Since, most of the services are digital, firms are able to keep their costs down and rely on technology instead of human capital.

By keeping basic fees very low or in some cases non-existing, the new generation of investors is more likely to invest with Robo Advisors than with traditional investment managers who typically require a substantial investment capital (sometimes a minimum of $100,000).

The Robo Advisory phenomena creates additional stress and pressure on the investment management community. As an increasing amount of people (especially young investors) take their finances in their own hands and deal with Robo Advisors charging lower management fees than traditional human Investment Advisors, we wonder what is the future looks like for an Investment Manager and/or a Portfolio Manager as a profession? If computers and algorithms are able to replicate and improve the component of asset selection, asset allocation and portfolio rebalancing, what roles will Investment Managers play going forward? Currently it is hard to know whether the field of Robo Advisors will survive in its current state in the next couple of years. According to The Economist, WealthFront has approximately $2.5 billion in assets under management, but made only around $7 million in revenu so far this year. With a payroll of +100 employees, the firm likely has expenses around $40 to $50 million. This means that to survive the company either needs to significantly grow its assets under management, increase its fees, or find alternative ways to generate revenue. Currently, WealthFront is being maintained by its investors who despite having invested nearly $100 million into the firm continue to lose money every year.

How many low cost providers can the Robo Advisory industry support? If WealthFront, the biggest Robo Advisor so far, with important venture backers cannot yet make a profit, what does it mean for young starts-ups rushing into this new field. Even if Robo Advisors end up taking a greater share of individuals’ asset allocations and portfolio rebalancing, human Investment Advisors still have an important role to play in personal finances and wealth management.

**1. Focus on long-lasting relationships**

Traditional Investment Advisors should focus on building long lasting and truly valuable relationships with their current and future clients. Some investment advisors only see their clients once a year to update their investment policy statements, rebalance their existing portfolios and make occasional changes for the upcoming new year. This can definitely change. If Investment Advisors consider themselves as real partners in their clients’ long-term goals and objectives, they can become more proactive and focus on constantly adding value throughout the year. If an investment advisor currently meets with her clients once a year, then setting up more frequent meeting like once a quarter would show the clients that she cares about them and their objectives.

**2. Maintain a constant communication**

Investment Advisors can use newsletters and quarterly reports to keep their clients educated about the latest development in their industry, changes to the tax codes, changes to the wills and estates procedure, etc,. By maintaining constant communication, Investment Advisors will become more aware of their clients’ short to medium term objectives and they can focus on providing timely information to their clients to help them make the most optimal decisions. Having the desired credentials like a Charter Financial Analyst will no longer be enough going forward to stand out from the competition and gain investors trust. Building and maintaining trust between investment advisors and their clients will take longer and will require constant presence and constant communication.

**3. Client Education**

What can make Investment Advisors and Portfolio Managers different from Robo Advisor in the future is emphasis on client education and helping clients see and understand the big picture. By helping clients understand complex relationships between various components of portfolio management and being able to clearly and simply communicate the intricacies of industry will help Investment Advisors add true value to their clients’ financial portfolios. In return, clients will feel like they are more engage in the process of managing their money since they will be more aware of how various investment strategies can affect their net wort, help them grow their assets and reach their financial goals.

**4. Move quickly**

The investment management industry is a behemoth. With over $30 trillion investment in mutual funds globally alone, it takes time for big institutions to move around and pivot. Although Robo Advisory is a relatively young trend, there are already companies like Upside who want to help investment advisors better manage their existing clients at reduced management fees. If Robo Advisors go mainstream, then traditional investment managers will need to embrace change to their existing ways of working with their clients and embrace new technologies and new services in order to stay ahead of the competition.

**5. Adapt to changing demographics**

Traditional financial planning usually looks at the long-term investment horizon. While older generations focused on saving for retirement and having a comfortable portfolio in 30 years, today younger generation is more preoccupied with short-term planing and shorter goals. For traditional Investment advisors to stay relevant, they need to understand the goals of the current generation (the so called millennials), who focus on technology, costs, accessibility, transparency and tend to be less patient. By understanding the demographic changes and structural changes in the employment landscapes Investment Advisors will be able to find areas where they can add value.

As stated above, the investment industry is bound to undergo tremendous change and disruption going forward. Robo Advisors are among the many important changes happening in the FinTech industry. It is imperative for young professionals getting into this field to understand that the traditional ways of working in the investment management industry are changing and that credentials like MBA and/or CFA no longer automatically convince people of your skills and experience. Only by understanding the changing behaviours and preferences of investors and by focusing on adding true value to their investors, will human investment advisors be able to prosper and build their investment practices going forward.

We hope you found this article useful and educational. We invite you to send your questions and comments using the comment section below.

If you are writing the upcoming CFA Level 1 exam, we invite you to purchase our CFA Level 1 Hacks and CFA Level 1 Starter Kit.

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]]>The post Everything you need to know about fixed income analysis, spot and forward rates, duration and convexity for the CFA Level 1 appeared first on Financial Analyst Warrior.

]]>Below we summarize the most important aspects of Fixed Income Analysis, Spot and Forward Yields, Duration, and Convexity for CFA Level 1 exam.

The value of a bond is the present value of its cash flows. If a single yield to maturity is given, you can simply use the following steps on your financial calculator to find the bond value:

N =number of coupons received

I/Y=yield per period

PMT=Value of each coupon payment

FV=Face value of the bond

PV=Price of the bond

If different yields apply to different maturities, each cash flow must discounted at the appropriate rate. This method is called the arbitrage-free valuation. Using the TD Bank 2.375% October 2016 bond rated AAA. We will use the U.S. treasury spot rates plus a spread of 0.71% which is the BofA Merrill Lynch AAA corporate spread to the treasury spot rate.

Unfortunately, we cannot input all these rates on the financial calculator. Discounting the cash flows at their appropriate discount rate yields a bond value of 102.13 which is very close the quoted price of 103 (as per Yahoo! Finance), the small difference could be the result of accrued interest and slightly different yields.

**Current Yield**

This is the simplest yield measure, it shows the investor how much he will earn in coupons from invest- ing in the bond today. Taking the TD Bank corporate bond from the previous section, we would earn $2.37 annually from buying this bond at a price of $103. This results in a current yield of 2.3%

**Coupon rate**

This shows the coupon payment as a percentage of the face value. Unless it is a floating rate bond, the coupon rate does not change during the life of the bond.

**Yield to Maturity**

YTM is the rate that makes the present value of the cash flow equal to the price of the bond. It cannot be computed easily since only a process of trial and error would allow us to compute the YTM. There- fore, the financial calculator must be used to find the YTM (I/Y).

The underlying assumption of the YTM is that the coupons are reinvested at the YTM which is not nec- essarily realistic since the reinvestment rate available to an investor could be different. This is the main limitation of YTM measure.

The bond equivalent yield is the semi-annual YTM multiplied by 2. When the bond is callable before maturity, the yield to call is calculated the same way as the YTM except the call date is used as the maturity. Also, the face value used is the call price which is usually larger than the 100 standard bond face value.

**Other yield measures:**

- Yield to worst: worst yield outcome (YTM or yield to call).
- Yield to refunding: YTM until the refunding date authorized by the bond covenants.
- Yield to put: Same calculation as the YTM but using the put date. Used only when the bond sells at a discount.
- Cash flow yield: Used for MBS and ABS and computed based on monthly cash flow and prepay- ment assumptions.

**Nominal Spread**

As outlined earlier, the nominal spread is simply the difference between the YTM of two bonds. It does not take the shape of the yield curve into consideration.

For example, the YTM of our TD Bank bond is 2.306% and the YTM of a Treasury note of the same three years maturity is 0.95%. Therefore the nominal spread is 2.306% – 0.95% = 1.356%

**Zero-Volatility Spread (Z-spread)**

When we actually computed the price of out TD Bank bond, we added a spread of 0.71% to all treas- ury spot rates to discount all six cash flows from this bond. This is actually the zero volatility spread which is a spread that is added to all maturities. This spread is superior to the nominal spread since it accounts for the structure of the yield curve.

For the level 1 exam, you are not expected to be able to compute the Z-spread. However, you know how to interpret it and use it to find the price of a bond just like we did in the TD Bank bond example.

**Option-Adjusted Spread (OAS)**

Since the addition of a call feature is detrimental to the bondholders, a higher yield will be required on a callable bond relative to an option-free bond. This extra yield will be captured in the Z-spread but is not related to the credit risk of the bond. Therefore we cannot compare the Z-spread of a call- able bond and regular bond. The OAS takes the option component out of the Z-spread for a callable or putable bond so that it can be compared to the Z-spread of option-free bonds.

When the bond is putable, the OAS adds the put component to the Z-spread. Remember that the put feature is favorable to bondholders and is therefore decreasing the yield required, thus decreasing the spread. To compare it to a normal bond, the spread must be increased to what it would have been without the embedded put.

We saw how spot rates are the rates earned on investments starting today at t=0. Forward rates are agreements to earn (or borrow at) a rate in the future. An investor who is expecting to receive some funds at a future date and is afraid interest rates will decline may enter the forward market to lock in a rate. Similarly, a borrower who expects to need funds in 1 year might lock in a forward rate in order to protect herself from rising rates.

Determining forward rates given spot rates does not require any formula. You should just find two equivalent investing strategies using the rates given. For example, if we are provided with the spot rates for 3 years and are asked to find the 1 year forwards ending year 2 and year 3.

The resulting time line would look like this:

An investor could implement the two equivalent investing strategies:

1. Invest for 2 year at y2 and receive (1 + y2)2 at the end of the 2 years, or

2. Invest at y1 for 1 year and reinvest the proceeds at f2 for another year. At the end of the 2 years pe- riod, the investor would get (1 + y1)(1 + f2 )

Therefore: (1 + y2)2 = (1 + y1)(1 + f2 ) (1 + 0.06)2 = (1 + 0.04)(1 + f2 )

f2 = 8.04%

Applying the same logic to find f3:

(1 + 0.07)3 = (1 + 0.06)2(1 + f3) f3 = 9.02%

In study session 15, we mention the interest risk as the potential decline in bond value following an increase in interest rate. In order to assess the magnitude of that risk, we need to know how much will the bond price drop with a given increase in rates. Duration is the preferred method since it is easy to use. However, the full valuation approach provides a more accurate picture of the interest rate risk of a bond or a portfolio of bonds.

**Full Valuation Approach**

This approach aims at computing the price of the bond given an interest rate scenario. For example, if the following non-parallel shift in the Treasury rates occurs, let us compute the change in price of our TD Bank bond:

Full Valuation Given Non-Parallel Shift in the Yield Curve

The value of our TD Bank bonds would therefore decrease from 102.13 to 101.11 if the illustrated yield curve shift occurs. This represents a drop of approximately 1%. The same approach can be used for a portfolio of bonds. The new rates will then be used to discount cashflows for all the bonds in the portfolio.

**Effective Duration Approach**

Duration is the change in bond price given a change in yield. However, the decrease in price given a yield increase is smaller than the increase in bond price following a drop in yield. This property is the convexity of the bond.

Since duration is different if the yield increases and decreases, effective duration computes it as the average between the two. There are various way to compute the effective duration of a bond but given the limited time given on exam day, the following method suffices:

For our TD Bank bond the effective duration would be:

With effective duration, we can quickly compute the change in bond value given an interest rate shift. For instance, if we expect yields to rise by 1%, the new price of our TD Bank bond would be:

Where D is the effective duration and it is negative because of the inverse relationship between bond prices and yields.

If it is easier for you, you may simply compute the price change in % given by and apply it to the old price. For instance, if the interest rates increase by 200 basis points, the new price will be computed as such.

**Macaulay Duration**

Macaulay duration is computed as the weighted average time period a bondholder receives his cash (including coupon payment and principal). If the bond has large coupon payments, the bondholder gets a larger share of his cashflow sooner and the duration will be smaller. If it is a zero coupon bond, all the cash will occur at maturity and the duration will be equal to maturity. This duration method is inferior to effective duration since it does not take into account the embedded options of the bond.

**Modified Duration**

Modified duration is calculated as Macaulay duration/(1+yield) and is therefore more accurate than the Macaulay duration. It is still not appropriate to use for callable or putable bonds. Effective dura- tion is the preferred method to compute duration and is the only method you should know how to com- pute for the exam.

**Portfolio Duration**

The duration of a portfolio of bonds is simply the weighted average of the durations of individual bonds in the portfolio. It is calculated the same way as portfolio beta if you recall from the equity ses- sion.

As we saw in our discussion on the full valuation approach, a non-parallel shift in the yield curve can make the duration measure inaccurate. For instance, in the current low interest rate environment, there is no scope for short term rates to decrease. Therefore, a decrease in interest rates would only affect longer maturity. Since duration offers a single measure of interest rate risk, it does not account for the fact that short term bonds` price will increase only slightly ad longer term bonds will increase more substantially. This limitation is exacerbated when analyzing the risk of a portfolio of bonds since all bonds will react differently to a change in yield depending on the maturity and other bond fea- tures. As such, portfolio duration only gives an approximate idea of the interest risk of the bond portfo- lio.

While duration assumes a linear relationship between bond prices and yields, convexity measures the curvature of the curve. Therefore, a more accurate estimate of the bond price change given a shift in yields would include convexity. Candidates are not expected to compute convexity but they should know how to use it to find an estimate of the price change of a bond.

As with duration, effective convexity takes into account embedded options such as a call or a put while modified convexity does not consider options.

**Price Value of a Basis Point (PVBP**)

This measures the dollar change in value of a bond given a 1 basis point change in yield (0.01%). Since duration already gives us the percentage bond price change in given a 1% yield, it is easy to compute the PVBP given the duration.

**Yield Volatility vs. Duration**

Duration measures the sensitivity of bond prices given a change in yield. On the other hand, yield volatility measures the frequency and magnitude of the change in yield. If a bond has a high duration and but a low yield volatility, it may be less risky than a bond with a lower duration but more volatile yield.

We hope you found this article useful for your preparation for the CFA © Level 1 Exam. For more valuable CFA © Tips we invite you to purchase our CFA © Level 1 Hacks.

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]]>The post Episode #8 | We cover 5 of the top 100 mistakes on the CFA© Level 1 appeared first on Financial Analyst Warrior.

]]>If you are currently studying for the upcoming CFA© Level 1 exam, then we invite you to check out our CFA© Level 1 Study Hacks as well as the CFA© Level 1 starter kit that features 100 top mistakes CFA© candidates make on their CFA© Exam.

On this episode, we cover 5 of those mistakes, namely:

– How interest rates influence exchange rates and how they affect the imports and exports of a country?

– How is share repurchase different from a dividend on shareholders’ value?

– What is the difference between Correlation and Covariance and what candidates need to look out for while studying for the exam?

– What is a structured note and how is it used in real life?

– The mistakes candidates make with one of Porter’s Five Forces (Bargaining power of suppliers)

– Bonus mistake

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]]>The Financial Analyst Warrior CFA Level 1 Bundle includes our CFA Level 1 Hacks Study Guide as well as our CFA Level 1 Starter Kit.

Your CFA Level 1 Hacks guide covers the most important and difficult concepts of the CFA Level 1 curriculum. In order to save you time, we don’t elaborate on the concepts that most candidates already know such as Time Value (for example).

We recommend that you use your CFA Level 1 Hacks as a supplement to your existing CFA Level 1 books and/or Schweser Notes.

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