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When learning about derivatives, we learnt about risk-free hedges and portfolios. However, one of the concepts was about borrowing and lending at the risk free rate. Now, for lending it's as simple as buying government bonds. However, how does one borrow at the risk free rate? I doubt it's about selling your own bonds. I'm just trying to work out how to apply these economic theories in real life, so any help will be greatly appreciated.

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  • $\begingroup$ Are you risk free? $\endgroup$ – user253751 Sep 21 at 11:32
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A private person will almost never have an access to borrowing at risk free rate. However, governments such as Germany or Switzerland can borrow at essentially for all practical purposes at risk free rate by issuing government bonds.

As a private person you might get access to risk free loan if you are rich enough to be able to negotiate the rate with bank and if your project is extremely safe (think of Jeff Bezos asking for small loan to build a private parking lot).

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    $\begingroup$ Banks can borrow at the overnight rate, this must be pretty close to risk free. Consumers can also borrow at 0% with some new car promotions. $\endgroup$ – lunar_props Nov 29 '19 at 1:48
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    $\begingroup$ @lunar_props The 0% promotions are tricky though, because you are borrowing on the condition of buying a product. I will happily sell you an apple for \$120 in \$10 monthly installments at 0% interest. $\endgroup$ – Giskard Nov 29 '19 at 5:38
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    $\begingroup$ @Giskard I agree with this. The 0% interest promotions are a bad example. $\endgroup$ – lunar_props Nov 29 '19 at 16:11
  • $\begingroup$ As I discuss in my answer, this argument is not exactly true. You can finance government bond positions at the repo rate, which is a risk-free rate. Yes, a repo is technically not a loan, but it is economically equivalent to a collateralized borrowing. Repo transactions are the glue that holds relative value trading in the risk-free curve. $\endgroup$ – Brian Romanchuk Sep 18 at 20:35
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    $\begingroup$ Apparently there are repo deals that are called "risk free." This paper discusses special repo rhsmith.umd.edu/files/Documents/Centers/CFP/ICIConf2013/…. Footnote 4 describes the concept of "haircuts" as a complication wherein the dealer cannot borrow the full value of the underlying Treasury security. Haircuts are efforts to price risk. $\endgroup$ – SystemTheory Sep 18 at 21:25
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It’s not normally possible for a private entity to issue a bond at the “risk-free” rate. (There’s been cases where bank curves traded below the sovereign curve - Italy in the 1990s - but there was perceived default risk.) However, it is possible to get leverage on a portfolio at the risk free rate. This is done via using repurchase agreements on central government bonds.

A repurchase agreement (“repo”) is a pair of buy-sell transactions where one party sells the bond “now” (settle date) and buys it back at a forward date at a fixed price. The rate of return on the transaction is known as the repo rate. (There is a need to post collateral.)

Selling and then buying is economically equivalent to borrowing at the repo rate using the central government bond as collateral.

E.g. buy \$10 million of a bond, then going into a repo transaction for \$10 million. You get the bulk of the \$10 million back, and have an economic interest in the bond (you buy it back at a fixed price at the end of the repo term). This is economically equivalent to buying it and using it as collateral.

Since the repo transaction is backed both by the bond and the counter party, it is technically safer than just lending to the government. As such, repo rates are considered a risk-free instrument, and trade in line with Treasury bills, etc. (with small spreads between instruments).

The fact that you can finance a bond position in the repo market explains why rate expectations is a useful valuation metric - the break even for profiting on a bond is the difference between the yield at purchase and the compounded repo rate. That is, it can be used in arbitrage.

If an investor has a portfolio that includes central government bonds, they can use the bonds as a funding source for leveraged positions.

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It is potentially possible although not initially. The transaction must be separated in at least two levels. Even if you are a normal person it could potentially work. L1 - lending money at a risk-free rate for the long term; L2 - purchasing a derivative and short-term borrowing using the debt as a collateral.

Outside of the main derivative transaction in question you should have purchased sovereign debt, i.e. gov. bonds of specific maturity. A caveat, not always individual investors have access to the sovereign debt market. Also from the return you should deduct the initial brokerage fee.

Then, when you enter the derivative contract you can additionally borrow from a bank the money needed, while posting the previously purchased securities as a collateral for the loan. Now if the banks are pricks, and they usually are, despite the soundness of the deal they will still wish to give you a non-risk free rate, although they theoretically should. NB! Sovereign debt can deteriorate, the bank is likely to request an additional premium in the form of percentage and fixed costs to add to the rate that you are likely to pay.

E.g.:

Purchasing a long-term bond i.e. 10Y+ could allow you to use the rate it pays, with the specific adjustments, for n-similar-month-cycles and engage in derivative transactions.

Your Net Profit = gain(loss) on derivate +/- income on the underlying instrument - brokerage fees +/- gain on the sovereign debt.

If you don't have at least USD/GBP/EUR 500k in your account, DON'T ATTEMPT THIS!!!

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I am sure you are aware that Governments often borrow at the risk-free rate. Now, this is because of the credibility possessed by the various governments. You do not expect the United States Government to default on its debt obligation, do you?

Coming to individuals, it will be difficult for a common man to possess that much credibility, which shall allow him to negotiate such a contract. Think from a commercial bank’s point of view, would you be inclined to lend an ordinary man at such a low rate? Another aspect of this, I believe, is that banks have a one track mind: maximizing their profit. Seldom, they would even consider lending at such low rates. This should hold, even if the chances of a default are incredibly low.

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A risk-free hedge is a deal made with a counter-party. These deals are promises all the way down and create counter-party risk which means they are not really risk free. See this article on the Money View of credit and debt relations which is different from the assumptions underlying modern finance theory:

https://lpeproject.org/blog/promises-all-the-way-down-a-primer-on-the-money-view/

Further, unlike the Money View, the Portfolio Choice Theory (such as that developed by James Tobin), which is at the heart of asset pricing models, entirely abstracts from the role of dealers in supplying market liquidity. These models assume an invisible hand that provides market liquidity for free in the capital market. From the lens of supply and demand, this is a logical conclusion. Since a supplier can always find a buyer who is willing to buy that security at a market price, there is no job for an intermediary dealer to arrange this transaction. The Money View, on the other hand, identifies the dealers’ function as the suppliers of market liquidity—the clearinghouse through which debts and credits flow—which makes them the primary determinant of asset prices.

Technically it is not possible for a risk producing venture to borrow at the risk free rate. However, as Warren Buffet explains (lost the exact reference) a well managed insurance company may have cost of capital below the risk-free rate. This is because the premiums charged for an insurance policy are capital for use in operations of the firm and the payouts for insurance claims are contingent future outlays. So if the insurance company can manage investment risk, costs, and actuarial risk it may have a cost of capital below the risk free rate.

I would add that the federal government in the United States tends to insure the ventures which would not be sound on an actuarial basis to provide long run profits to a profit-motivated insurance firm. These government subsidies include federal loan guarantees, flood insurance, and deposit insurance. During the so-called global financial crisis starting in late 2008 the Federal Reserve had to take over AIG derivatives book and the US Treasury became conservator of Fannie Mae and Freddie Mac. Perry Mehrling calls the central bank the financial dealer of last resort and I refer to the US Treasury as the investor of last resort. If the counter-party has a cash flow crisis or must be resolved due to insolvency then the risk-free hedge deal suddenly has "fat tail" default risk.

This article provides a "narrative" for the demise of AIG as financial dealer with lack of liquidity in a financial crisis:

https://insight.kellogg.northwestern.edu/article/what-went-wrong-at-aig

The global financial crisis and its resolution is a case study which tends to validate the Money View wherein financial dealers use their balance sheets to create liquidity and these dealers run out of liquidity when there is a general panic of investors who hold the liabilities of the dealers (rollover risk). The risk-free hedge will have "fat tail" risk whenever the counterparty runs out of balance sheet in the network of financial deals.

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