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Risk-free rate is that you get for letting someone else use your money in a riskless manner. Suppose we live in a world where there is no risk whatsoever. In particular, if you lend someone \$100 there is 100% certainty that he will pay you back in a year. Before the pay date, he can do whatever he wants with your$100, while you have no access to it. Even ...

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Actually, overlapping samples is a big problem in financial machine learning which is called concurrency. Marcos Lopez de Prado discusses this issue in Chapter 4 of his book Advances in Financial Machine Learning Ideally, non-overlapping returns should be used to train the model, however this constraint massively decreases the length of your training ...

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You say: At this point I don't really get any further, as I am unsure about which "cross section" is being talked about here. Since I have created 25 portfolios, I can only have all in all 25 values in the cross section, right? Isn't that far too little for a sufficient regression? Or do I have to run new time series regressions for each company ...

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U.S. Government DID save American International Group (AIG) from bankruptcy, since it was considered too big to fail, actually: a lot of financial institutions were insured by AIG. This Investopedia page is a nice summary on the topic about AIG's bailout. Here (Investopedia again) about Lehman Brothers, that became really too much leveraged and exposed to ...

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The definitions will vary from organization to organization but generally: Wealth Management is the management (either direct or through distribution to other managers) of an individual investor’s money with an emphasis on service and client relations Asset Management generally can describe both managing individual assets (like Wealth Management) and ...

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You may be over-thinking it. It is a straightforward calculation using matrices, as easy as turning the crank of a sausage-making machine. The standard deviation matrix is |0.16 0 0 | S = Diag(s) = |0 0.15 0 | |0 0 0.04| The correlation matrix is |1.0 0.5 0.2| R = |0.5 1.0 0.0| |0.2 0.0 1.0|...

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The risk free rate is important and the reason for the inclusion and consideration of the risk free rate is that investors do not get compensated for not taking on risk. Now, we can argue whether the risk free rate truly provides risk free returns (we all should know that it does not, but ...) but it is important in the context of pricing risky assets that ...

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In my opinion, risk free rate is not necessarily positive and not so important to pricing theory. It happened to be positive in most cases, but imagine a planet using Uranium-235 instead of gold as the money and unknowingly suffers from a shrinking population, likely the risk free rate is negative. Below are what I regard as important in pricing theory, ...

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My non-rigorous answer: The future is uncertain. Even if there is no financial risk to investing in the "risk free" asset there is personal risk. For example, I could get hit by a car and die. Even if I survive till the moment that I liquidate my investment I will have less time left in my life to enjoy it. I need to be compensated for giving up this ...

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High level Flow of funds comparative analysis for the U.S., Japan, and Euro Area by the bank of Japan. Country level report from the ECB. It is an 800+ page report so the link may take time to load (alternatively go to ECB data warehouse/reports/Euro Area accounts). Canadian financial flow accounts data.

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Regarding how the rating agencies gave AAA ratings to CDOs and the like that clearly did not deserve those ratings - straightforward answer. The SEC licences all the ratings agencies as "nationally recognized statistical rating organizations" (NRSRO). It is blindingly obvious that the SEC was not actually overseeing the rating organizations that it was ...

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MBS are securities which represent ownership in a pool of mortgages ABS are securities which represent ownership in a pool of assets other than mortgages (for example auto loans or credit card loans) Collateralized Debt Obligation are complex entities which issue tranches of securities to investors and use the proceeds to buy MBS, ABS or other assets. The ...

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Conceptually, a par/par asset swap may work as follows (details can always be customized): At trade inception, you buy a bond priced at $P + AI$. You pay 100 out of pocket (or via a repo). The residual amount, $P + AI - 100$, is obtained with a swap dealer as an asset swap. After the trade has been initiated, the coupon payments received from the bond are ...

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First of all, your nonlinear problem involving $max(-w_i,0)$ is still convex albeit inconvenient for standard solvers due lack of smoothness. In addition to the slack variables mentioned in the comments, the problem of constrained short exposure can be cast in a convex form as follows: $$w=argmax(\mu^Tw)\quad s.t.\quad w^T\Sigma w=R,$$ under the ...

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The investor wants to spend 100 on an investment and then receive a floating coupon equal to Libor + some spread. So, investor purchases a bond with price 99 and then does a swap where they pay an extra 1 upfront (thus, total payment =100) , then pays the bond coupon and receives Libor + some spread. Those are the mechanics.

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Let's consider a single cash flow CF $PV = (\frac{1}{1+i})^n CF$ As you wrote $v = -\frac{1}{PV} \frac{d PV}{di}$ Taking the derivative of PV with respect to i and plugging it in: $v= - \frac{(1+i)^n}{CF} n \frac{1}{(1+i)^{n-1}}\frac{-1}{(1+i)^2}CF$ after simplifying we get $v = \frac{1}{1+i}n$ (which is easy to remember, no need to derive it every ...

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I suggest to distinguish three things: Why risk-free rate? What defines its magnitude and sign? And what is its role in specific economic models? "Why risk-free rate" is very simple to answer: Because you want to compare cash at different points in time. One assumes that the difference between cash at time $t_1$ i.e. $C(t_1)$ and at time $t_2$ is $C(t_1) - ... 1 There are a number of different ways to accomplish your goal. One would involve modelling each financial time series and then connecting these marginal distributions using a copula. Monte Carlo is then a matter of simulating the marginals and the copula. In using your Cholesky matrix, you are implicitly using an elliptical distribution (think of Gaussian ... 1 To find the weights in the question (a) you should write your portfolio expected excess return and variance as: $$E[R_p^e] = w_A R_A + w_b R_B - R_f \\ \sigma^2[R_p^e] = \sigma^2[w_A R_A + w_b R_B - R_f] = w_A^2\sigma_A^2 + w_B^2 \sigma_B^2 + 2 \rho_{AB}\sigma_A\sigma_B$$ The sharpe ratio is given by: $$S(w_A,w_B) = \frac{E[R_p^e]}{\sigma[R_p^e]}$$ So, ... 1 I am not sure you have the same definition of bootstrap than myself: bootstrap is mainly a way to estimate the variance of estimators when you do not have a closed form formula to obtain it directly (thanks to Efron's theorem). It means if you want the variance of your estimator of returns or covariance, you could use bootstrapping. Bad news: if you ... 1 Well I think the main issue is that the BMIS had no external party acting as an official holder of the books and records. The Asset Manager utilizes a broker to get access to the market, and the Custodian (and the Administrator) to be the official keepers of the books and records of the trades, by validating and confirming the execution of each trade. Both ... 1 Asset product = Weighted sum of the product of the three assets. You can write the following Since:$A = \omega^A_1.A1+\omega^A_2.A2 +\omega^A_3.A3 $And$B = \omega^B_1.A1+\omega^B_2.A2 +\omega^B_3.A3 $You can develop$E(A.B) $from there as a linear combination of the mean and variance couple for the three assets... Therefore, the formula for$cov(...

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You can solve for the covariance of the two portfolios and since you have E(A) and E(B) you can back into the E(AB)

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You're right about the equity value increasing with higher volatility. You're wrong about the debt value. That decreases with higher volatility, because it is short an option. And yes, equity holders have an incentive to increase volatility, at least in that model.

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Yes, the new investor could have a opportunity. This is "normal" life. Launching a new fund is a possible way, but it is expensive (as you indicated). Sometimes it is necessary to launch a new fund: when fund restrictions are in place. Example: In your question, the investment of the new investor will shift the asset allocations from 40% (AAA), 40% (BBB), 20%...

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The expected return of the portfolio is just the weighted sum of the expected returns of the assets, i.e. $$R_P = w_1\cdot R_1 + w_2\cdot R_2 + w_3\cdot R_3,$$ where $w_1, w_2, w_3$ are the porfolio weights and $R_1, R_2, R_3$ are the expected returns for the assets.

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Your broker will keep track of this information. Each order creates what is called a tax lot. TD Ameritrade explains it as follows: Each time you purchase a security, the new position is a distinct and separate tax lot — even if you already owned shares of the same security. (A tax lot is a record of a transaction and its tax implications, including ...

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APT assumes that idiosyncratic risk is zero on average: $E[e_i]=0$. The law of large numbers. From 1 and 2 it follows that as N increases, the weighted sum of idiosyncratic risks will converge to zero: $\lim\limits_{N\to\infty}\sum\limits_{i=1}^N e_p=\lim\limits_{N\to\infty}\sum\limits_{i=1}^N w_ie_i=0$ Strictly speaking some restrictions on the weights ...

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Edited: The risk free rate is positive because the factors of production, and the perception of time (from an individual's perspective) are limited. Limited supply of desirable goods such as houses (or limited capacity to make them from land, labour and capital), gives them a positive value in society (versus say air, which is in almost unlimited supply, ...

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A risk free rate is the return rate from investing in an asset that has the lowest risk found in the market. It is a naming convention. The least risky of all returns is labelled as 'risk free' for the purpose of various models and resulting discussions. Another parallel answer is that you must understand what financial risk is in the first place. It is, ...

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