More Discussions for this daf
1. Loaning for "ten years" 2. Eidim Zomemim That Are Mechayev A Kesuvah 3. Valuation of the Kesuvah according to Rebbi Nasan
4. Edim Zomemin not a Kenas? 5. Calculating risk factors in the Kesuvah 6. Edim who lied about the date on the Shtar
7. Edim Zomemim 8. Measures 9. Edim Zomemin

yoel steinberg asked:

tosfos gives illustrative case of tzad ha'ish as being worth 50; tzad ha'isha as being worth 40; the ksuba itself being worth 100. the value of of tzad ha'ish without there being any tzad ha'isha at all is the full amount of the ksuba. if tzad ha'ish is anything less than the full 100 it is due to tzad ha'isha. if so why doesn't the 50 of tzad haish and the 40 of tzad haisha add up to the 100 of the full ksuba amount? where did the missing 10 go to? tosfos doesn't say.

from a finance point of view the missing 10 is explained by what is called a "risk premium". as nemukai yosef says here, "ain adam mesakken ma'ossav bchinam". i think what he means is that a gamble sells for less than the "expected value" or "actuarial value". what that means is illustrated by the following example.

you may flip a coin and win a million dollars if the coin lands on heads (or tails) if you guessed correctly in advance of flipping the coin. how much would you pay for this gamble . how much would you really pay , not just as a theoretical cheshbon?

you might say that it's a 50/50 chance of winning the million, so the gamble is worth half a milllion (see igros moshe regarding the worth of a raffle regarding maaser ksaffim). however you personally would not gamle half a million since it's a big amount of money to take chances with even if you might win a million. so the price of such a gamble goes for let's say 350,000. you don't want to risk your money for only the amount that is the expected long term winning, unless you get the gamble for a cheaper price. as nemukay yosef has it, a person wont take a risk unless he gets a payoff more than the expected payoff for the amount he risks. ain adam mesakken maossav bchinum.

in our coin example, the "tzad" of heads should have been half a million, but because of risk premium it sells for only 350,000 . 150,000 dissapeared from the market value because of risk. similarly, on the "tzad" of tails 150,00 dissapeared because of risk premium. In all, 300,000 dissapeared because of risk.

So too by ksuba. the tzad Ha'ish really works out to an expected (or actuarial) value of say 56. but because there is a risk of losing on the tzad ha'ish, the investors want to pay only 50 for it.

similarly by the tzad ha'isha: it really works out to be worth lets say 44. but because of risk, the investors want to pay only 40 for it. 56 + 44 does add up to 100. but 10 dissappears from the total because of the risks involved in gambling on either tzad haish or tzad haisha.

going back to the coin example, if you would be a wise guy you could buy two gambles each one going for 350,000 as described above. but instead of betting both on heads, or both on tails, you could bet one on heads and one on tails. you paid a total of 700,000 for both gambles. the coin is flipped only once, so you would DEFINITELY lose one gamble, and DEFINITELY win one gamble. you would pay 700,000 and win a million. you profitted 300,000. you did so knowing in advance that you would win were someach bchelko to accept 300,000 instead two million that you might have had if you would have guessed right on both gambles. ( a "teich" on ezehu ashir hasomeach bchelko" by being someach bchelko, you became rich. you made 3000,000, and you you did it again and again forevery two bets you made.) such a trick is called "arbitrage".

applying this to the gmara here, it shows what principle the amorayim are argueing about. it is not a machlokkes metziuss of how to calculate the value of the kasher zommam. it is a machlokkes in principle of how far does it apply. the husband was in a position to do an arbitrage by buying the tzad haisha. (as rashi has it the baal will buy tzad haisha "bratzon". why "bratzon"? because he will be setting up an arbitrage. ) he could have but didn't do it yet. if he would have he would be in a position similar to you were when you bet on BOTH heads and tails. you won the amount of money which dissappeared because of risk. you arbitraged away the risk and won it. so too the baal. he could have arbitraged by buying tzad haisha. he would have won that 10 which dissapeared ( which dissapeared because buying a zchuss ksuba is a gamble)

the machlokkes amorayim seems to be whether kaasher zommam applies even to an OPPORTUNITY to make money in a 100% secure investment (i.e. an arbitrage) as opposed to maybe making more on a risky investment. bs"d

yoel steinberg, boro park brooklynamerica

The Kollel replies:

The first part of your dissertation sounds fairly obvious. The fair value of each one's rights must be less than half of the total even if the chances of receiving the field are indeed fifty- fifty. If not, why would anyone pay that value instead of keeping his money?

However, I do not follow your claim that the husband has made himself the owner of a risk free investment (arbitage) for the following reason:

Before the husband invested in buying his wife's Kesuvah, there existed two possibilities. Either he would not have to pay it at all (if she dies first), or he would have to pay the entire Kesuvah (if he dies first). By buying his wife's rights in the Kesuvah he is protecting himself against the possibility of having to pay her the entire Kesuvah at a later date. But he is paying a premium for this "insurance": namely, the amount that he spent on buying the wife's rights to the Kesuvah. True, the "premium" might be less than the market price for such insurance; however it is certainly not an arbitrage, since by paying the premium he is now forgoing the chance to "win" the entire Kesuvah for himself without spending a penny.

D. Zupnik

Yoel Steinberg asked:

Regarding what we discussed- when the husband starts out, his stake is worth fifty as tosfos has it. regardless of what he may win or lose, that position is worth fifty.

before buying tzad isha, though he did have a chance to win the entire ksuba, he also had an offsetting risk of paying it. you might want to view the husband as having been in a loss free position of maybe winning or not winning. but regardless of how you view it: whether you view the husband as being in a position of risk, or if you want to view buying tzad isha as paying insurance, his stake was worth 50.

after he has bought the tzad isha, his stake is now worth 100. he has increased his stake by 50 with a 40 purchase price. he has profited 10. he did this by making the risk disappear. (for him anyway)

That is if he actually does buy the tzad isha.

(buying both sides of the ksuba is an arbitrage situation since this creates profit by making certain risks disappear. this can theoretically be done with money that is borrowed in the morning and paid back in the afternoon, before any interest has time to accrue: borrow 90; buy both sides; sell [short] for 100 the entire ksubba including the immediate income stream of the peyrose which is part of your tzad ha'ish; pay back the 90; profit 10. all in a few minutes on the open market.)

the first part is not so obvious though Baruch Hashem you may think it is. the geonim brought down by the rishonim seem to give a very different description of how to value a ksubba. seems ramban was the earliest of the meforshim to state the estimates and machlokkess amorayim using an economics idea. (please tell me your opinion of what rav moshe's psak is. he doesn't spell out whether he accepts this idea. he gives the example of the tzeddaka selling 5000 raffles to win 1000$. he simply says "shavyo yadua")

looking further in milchammos, he explains machiokkes between second and third amorayim (regarding nichsei melug) as whether the hazzamah victim need be muchzak in the attempted damage for kaasher zommam to apply. perhaps to a degree this is what first two amorayim also argue over regarding the 10 (50 vs 60). the certainty of winning the "extra" 10 is only at the bottom line. but on either side of the arbitrage (tzad ish or tzad isha) neither outcome is a muchzak. (muchzak here used in the sense of as opposed to royui) . perhaps that machlokkes would also apply if zommemim said a son is not a yoresh while the grandfather is still alive. would the zommemim need to also pay for the grandfather's estate which is a nachla habaah l'achar mikan?

By buying tzad haisha, the husband is not forgoing the right to win the ksuba in case the woman dies before he does. he will collect the ksuba in such a case whether he buys tzad isha or not. as far as his spending money on the "insurance", he is getting something for it. actually insurance here is not a complete description of what he is buying, since there is an open market for him to resell it on. he is not paying a premium; he is buying something considered equivalent to money. (for kaasher zommam anyway)

ANOTHER POINT: if your asset appreciates by a quantifiable amount, but that appreciation is not liquid, do you include that appreciation on your balace sheet?

or: would kaasher zommam apply to a defineitely quantifiable but illiquid asset?

rashi seems to explain the machlokkes amorayim regarding the extra 10 (50 vs. 60) depends on whether the ability of the wife to possibly sell her contigency ( by cedeing the ksuba policy) should be accounted for in the calculation of the Kaasher Zommam damages.

"d'shema... hi lo timkorena lo btovas hannoa"

the man's assets (which the zommemim attempted to harm) can be valued at 60 if we account for the arbitrage opportunity that theoretically is available to him. his assets are worth 60 from this point of view. but he won't neccesarily realise this value since the asset is not liquid due to the perogative of the wife not to sell even at market value.

the liquid value of the asset they attempted to damage is only 50.

Yoel Steinberg

The Kollel replies:

You write that "buying both sides of the ksuba is an arbitrage situation since this creates profit by making certain risks disappear. this can theoretically be done with money that is borrowed in the morning and paid back in the afternoon, before any interest has time to accrue: borrow 90; buy both sides; sell [short] for 100 the entire ksubba including the immediate income stream of the peyrose which is part of your tzad ha'ish; pay back the 90; profit 10. all in a few minutes on the open market."

If you know of such an open market, please tell me about it; it seems like a trader's dream. Let us put your story in practical terms and scrutinize the actual potential for profitability (as must always be done before engaging in "sure-fire" opportunities):

After the purchase of the Tzad ha'Ishah, the Ba'al is now holding both sides, which means that he now will end up with the money at the end of the term notwithstanding. This has cost him a bird in the hand (40). Ostensibly, we could say that his position is worth 100, although it is only worth 100 to him, for he is the party who has exposure.

However, if he were to go and resell the Tzad of the Ishah alone he would only recoup his 40, and would again be exposed. If he were to sell his side only, then he would take in only 50. If he would sell both sides, then he would not get anything; there is absolutely nothing to sell since both sides together do not give the buyer any rights whatsoever. If the Ba'al dies first he will have to pay himself and if the Ishah dies first he will not have to pay himself. Basically, if you own both sides, the Shtar is Batel. As for the rights to the Peros, they now are unlinked to the Shtar for as soon as the Ba'al has no Shi'abud -- since he owns the Tzad ha'Ishah -- there is no linkage of any Karka to the debt.

D. Zupnik

Yoel Steinberg writes:

Rabbi Zupnik,

Susquehanna Capital was written up in Wall Street Journal about 15 years ago in the Wall street Journal. What they did was trade with cell phones and laptops on their backpacks setting up arbitrage using floor traders on different exchanges (NY Chicago etc) to capitalize on momentary discrepancies in stock prices to long at one exchange and short on the other. I interviewed with them over the phone.

Bs"d i traded commission free bond mutual fund using a model similar to what attributed to the Milchammos. Bonds sell at a discount to their expected value on the close of trading before the monthly CPI report is out. (also for other inflation related reports). Buy with 1/8 of portfolio each month. End up on average with the expected value. The difference is the trading profit. Sold out the day the report was released and bonds went back up.

(Other techniques also , overreaction to forward looking reports which tend to be ignored a little after while; old news not as dramatic as it was when just came out. If the report was inflationary doubled the bond portion to 1/4 from 1/8 then sold out at break even or profit when bonds recovered. yield was around 18% with position in cash most of the month. This worked when inflation fears was an issue for the bond market. around 11? years ago.)

The description of longing and shorting ksubbos was to illustrate the idea was trying to explain. Lav Davka that there are open markets for ksubbos.

I think the key to Rashi's Shitta in explaining what the Machlokkes is about are expressed by the quote i emphasized: ' "d'shema... hi lo timkorena lo btovas hannoa". In general, Tashloomei Hezzek would need an ascertainable market value of the (sale or) damage for it to be recognized. ( A classic illustration is Nesivos'[?] explanation why buying Meoras Hamachpella was not a Mekach Taus, despite it's historical value as the burial site of Adam and Chava. Since no person besides Avraham knew of this, the cave did not have this calculated into its market price. A monetary value must have the potential to bring a sale. A value that will not be reflected by the market is not recognized.) By the ksubba sale, the extra 10 for Tzad Ha'ish does ,on the one hand have a monetary value reflected on the market, since by calculating via Tzad Ha'isha this is what the Tzad Ha'ish comes out to. The Tzad ha'ish is an asset for sale on the market. On the other hand, the needed steps of this calculation (i.e. the tzad Ha'isha) are not (not necessarily at least) for sale. "d'shema... hi lo timkorena lo btovas hannoa".

Regarding what you wrote on the economics (you didn't explain how this is a tirutz or kashya on what i wrote to explain the sugya): The baal can sell the karka itself since (after buying tzad isha) he has the kinyan hagoof (which he had since before he married to begin with) along with the kinyan haperose (which he retained in the tzad ha'ish) and there is no longer the "call" (a term from options trading) on the karka to deliver it to the wife in case the ksuba must be paid. In effect, the man fully owns the land as any other land he owns.

This position of full ownership is an improvement over his situation prior to buying tzad Ha'isha. The monetary value of this improvement, as calculated using assets with a market value, is 10.

He should not sell Tzad isha or tzad ish. Doing so would be de constructing his arbitrage position- a common mistake of traders under pressure who change their mind thinking they will profit on both sides of a straddle. He should sell the karka ksuba itself for 100 and be satisfied with his safe profit of 10.

(even if it would be a case of a situation in which he can't sell the karka -which is not the case here- such a situation is what the amorayim are arguing about. he has an asset calculated using values from the market, but he can't necessarily liquidate. As that Rashi says "d'shema... hi lo timkorena lo btovas hannoa".) The Taana you were trying raise, in opposition to what i wrote explaining the reason for 60, is the reasoning of the other shitta that holds it is 50. But that is what the Machlokkes is about.)

The Igross Moshe seems to go not like the Milchammos. "shavyo yadua" seems to be that he divides the $1000 by the 5000 raffle tickets to make each worth 20 cents. If the tickets would need to be discounted for risk premium, why would their worth be yadua? how much is the discount? 1 cent? 2 cents? 9 cents? Rav Moshe didn't spell it out in the Tshuva. Trading professionals use some formula (black scholes etc..) to determine what the market sets for the risk premium, but how yadua is that? (besides it gives only an estimate, and is a tzarich iyun in itself) Maybe Rav Moshe was going lchumra because it's maaser ksaffim and the possibility of buying all the tickets should be reflected in pricing the tickets even when the donation is for only one ticket.

p/s are you the Rabbi Zupnik from Passaic? either way, Shalom Alechem.

Yoel Steinberg

The Kollel replies:

Your examples of arbitrage are interesting, but not relevant to the present discussion. What I meant was the following: The husband cannot sell both sides of the Kesuvah (as you understood). If he sells the land that was designated for the Kesuvah, that is not equivalent to selling the Kesuvah; it is simply selling the land. Remember, the land is not the Kesuvah itself; it is merely an asset which it is Meshu'abad for the payment of the Kesuvah.

If you insist on using market examples, compare it to buying back a short covered call which then allows you to sell the underlying, which is not part of the value of the call.

As for risk premium (per Mr. Black and Mr Scholes whom you mentioned), as a raffle ticket has no intrinsic value (no volatility), and I'm sure the interest is not factored in, clearly the value is all for the *chance to win*. The true market value should therefore be calculated by what the market is willing to pay. Clearly we see that the market price is more dependent on the possible profit than on the chance to win. (A case in point is the big ticket lotteries, in which people will pay more for a ticket (on a secondary market) even though the chance of winning is smaller since the dollar buys you more dream.) The same is true for Hail M. out of the money options, which should be worthless but the chance of scoring on the big time can drive their price up (besides their value as a hedge etc.).

(Rabbi Zupnik from Passaic is my brother, who unlike me has spent his time learning and has no idea what arbitrage is.)

D. Zupnik