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38

Very obscure historical example: From 1287 to 1295, the Danish nobleman Stig Andersen Hvide was leading a band of outlaws from the island of Hjelm supported by the king of Norway against the king of Denmark. Stig managed to kidnap expert coin makers and bring them to Hjelm, where they produced counterfeit Danish coins. This allowed Stig and his supporters to ...


29

https://en.wikipedia.org/wiki/Operation_Bernhard (an exercise by Nazi Germany to forge British bank notes. The initial plan was to drop the notes over Britain to bring about a collapse of the British economy during the Second World War. )


12

David Petruccelli writes in "Banknotes from the Underground: Counterfeiting and the International Order in Interwar Europe" In December 1925, a group of Hungarian nationalists were caught trying to put into circulation a large quantity of counterfeit francs in a bid to weaken the French economy and fund irredentist action in Central Europe. Edit: ...


5

Examples where this happens are always extreme and contrived. I can think of two kinds of examples. The first is where you have an asset that for some reason has a price of zero or negative but a positive payoff in some states (perhaps no other asset pays off in that state). The second is where you have two assets with positive prices that have negative ...


5

Net Present Value (NPV) as a soft concept existed probably even in antiquity but it was formalized and made popular by Irving Fisher in his book the Rate of Interest. Internal rate of return is basically a special application of NPV. It was also first formally introduced in Fisher's book although he called it 'rate of return over costs'. Duration of bonds ...


5

...the completeness of markets implies that the stochastic discount factor is strictly positive... This statement is not quite correct. Rather, the agent's optimality condition implies that market is complete with respect to the agent's consumption-relevant states, and that the SDF must be strictly positive on those states. The SDF is, more or less, same as ...


5

...no-arbitrage models (such as Black-Scholes and HJM) are equivalent to equilibrium models (such as CAPM or C-CAPM). Short Answer Yes, for models where asset prices are assumed to be Ito semimartingales (where the martingale part is a Brownian integral), although a more general argument is needed than that suggested by the special cases typically ...


4

In mean-variance optimisation I have typically seen the below quadratic utility function where $𝐸[𝑅]$ is the expected return (or mean return) of a possible portfolio, $\sigma^{2}$ is the return variance of that portfolio and $A$ is a parameter that the determines the sensitivity to variance. $$𝑈=𝐸[𝑅]−\frac{1}{2}A\sigma^{2}$$ As an aside, maximising % ...


4

Several articles use data sets on this issue but I am not sure that all the data sets are freely available. Valencia & Laeven (2012) use the IMF country reports to create their data set. It covers all IMF member countries since 1970. EDIT: it is available here, as pointed out by @dismalscience. Reinhart and Rogoff (2009) have 70 countries since roughly ...


4

(Looking at the question and notation used more closely, the formulation seems to be problematic in couple places.) General Fact Let $W$ be standard Brownian motion with respect to filtration $( \mathscr F_t )_{t \in [0,T]}$. Consider $(L_t)_{t \in [0,T]}$ defined by $$ \frac{dL_t}{L_t} = \psi_t dL_t, \; L_0 = 1. $$ In general, $L_t = e^{\int_0^t \psi_s ...


3

This question cannot easily be answered. If we look at historical societies, bond markets appeared in eras where was a central bank, most importantly, the Bank of England. During the Gold Standard, notes were not 100% gold backed. If we look at earlier eras, customs were very specific to a culture. For example, there were eras which were largely non-...


3

A checking account is considered a liability because bank essentially owes the amount on the checking account to the owner of the account. If a bank loans someone money that is considered an asset on the banks balance sheet but if that person decides to open checking account at the same bank checking account becomes liability. The loan will still be ...


3

For starters, I've confirmed your results for the United States using data from federalreserve.gov and alfred.stlouisfed.org: If we take a look at the breakdown of bills in circulation, we can see that the value of $100 bill has drastically increased relative to the total value of bills in circulation but the others bills have not. So people are indeed ...


3

This was most likely reference to the Fisher hypothesis. As argued by Engsted & Tanggaard (2002): classical economic theory, especially the Fisher hypothesis, according to which expected nominal asset returns move one-for-one with expected inflation such that expected real returns are independent of expected inflation. A related implication is that ...


3

As of the market close on 2/14/2020, Apple's stock price was \$324.95 per share. The forward looking dividend (based on announced dividend policy over the next year) is \$3.08 per share. The forward looking dividend yield is therefore $\frac{3.08}{324.95} = 0.00948$ or 0.95%. This means that for every share, the firm is planning to pay out \$3.08 over the ...


3

Repo is the short abbreviation for Repurchase agreement, as per Investopedia (https://www.investopedia.com/terms/r/repurchaseagreement.asp).


2

Here are the papers I've already found, in chronological order. USA Boskin, Michael J., et al. "Social security: A financial appraisal across and within generations." (1986). Boskin, Michael J., and Douglas J. Puffert. "The financial impact of social security by cohort under alternative financing assumptions." (1987). Duggan, James E., Robert Gillingham, ...


2

A great starting point is "Fundamentals of Corporate Finance", Ross, Westerfield & Jordan. This book will give you a good overview of key concepts in finance. This book is widely used in introductory courses for non-finance majors, to both teach some fundamental ideas, and give a panoramic view of the field. "Trading" will probably be the topic that ...


2

Let $L$ be the loan amount, then $L=P\frac{1-(1+i)^{-n}}{i}$ The balance at time $t$ is defined as the present value of the remaining payments, $B_t=P\frac{1-(1+i)^{-(n-t)}}{i}$ By using the following equations $I_k+C_k=P$ and $I_k=iB_{k-1}$ where $I_k$ is the interest paid at time $k$ we derive the following equation $C_k=\frac{P}{(1+i)^{n-k+1}}$ and ...


2

I assume EBT = Earnings before tax. Take a \$200 project with a 6% return on assets. If 109% equity financed, EBT = \$12 (6% return). If debt has a cost of 5%, and 50% financed (\$100 borrowed), earns \$12 - \$5 = \$7, or a 7% return on equity. So the rate of return is higher, even though total earnings are less. However, if interest were not deductible, ...


2

While people are spending less, they are also earning less, especially the many millions who have lost their jobs. It is very possible that the earnings lost are much greater then the money saved on reduced spending, and so net savings will decrease. It will take time before we really know either way. Here is a study which looks at the increase in savings ...


2

It’s a chart of the underlying stock. It does not show anything about options.


2

There are a lot of differences between the two crises + how these differences manifest in the stock market. First, on the point of the stock market- it's "kinda" an indicator of the overall economy. However, it's not a perfect metric; really, it reflects the weighted sentiment of those who participate. Furthermore, the stock market is more akin to ...


2

The logic given in the question is inadequate, since it misses the point that upside potential in long option positions is much higher than the upside potential for a short option position. If one were buying/selling options at fair value on instruments that followed the random process used to price the options, a long or short position should not have an ...


2

Dividends have to be taxed as income, as otherwise people can incorporate, have their wages taxed as revenue for the corporation, and then pay themselves a dividend. (Canada adjusts taxes on dividends in an attempt to make these two approaches equivalent for taxes purposes.) Capital gains are at a lower rate for reasons that are debatable. However, in order ...


1

It’s a 2x levered ETF. It has an exposure that is -2 times the size of the fund. The exposure determines how much the fund gains or loses in response to a change in the underlying asset. Since the exposure is 2x the assets in the fund, the exposure needs to reset daily. That is what the table demonstrates.


1

A repurchase agreement (or repo) is the sale of securities for cash, but with a commitment to repurchase them later at a specified price at a future date. This is practically a collateralized loan, and I find it conceptually helpful to think of it that way. If you are taking out the loan, it's a repo for you. You are agreeing to repurchase the security (...


1

This question implies to me that you want to convert historical incomes to “2020 dollars”. The standard way to do that is to use the consumer price index (CPI). Note that this is the level, not the rate of change (“inflation rate”). The formula for a year T is straightforward: (Income in “2020 dollars”) = (income in year T) *(CPI index in 2020)/(CPI in ...


1

I cannot really follow your formulas, what is the logic behind them? Seems to me there is no way to divine three state risk-neutral probabilities from 1 financial instrument's prices. The equation $$ p_1 288 + p_2 180 + (1 - p_1 - p_2) 120 = 180 $$ is underdetermined, there are infinitely many solutions to it. Now if you solved the equation system $$ \...


1

The simplest way to understand this is to write out the numbers for a particular loan. You can track the balance, and interest over time. Very easily done in a spreadsheet. The amount of principal repaid in each payment is increasing as time passes, as the amount of interest paid falls (since the interest is proportional to a falling principal balance).


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