How Risk-Free Portfolios Can Be Built from Risky Assets

# What assets other than bonds are risk free?


# What assets other than bonds are risk free?












I saw a question the other day that said

> Assume you have only two assets to build a portfolio. Name and explain three scenarios under which a completely risk-free portfolio can be formed?

I have a few questions:

- Is this poorly worded? Surely there are no assets that are completely risk-free. Should this be written as "virtually risk-free"? If not, how can an asset have absolutely zero risk?

- The only assets I can think of that would be virtually risk-free are AAA-rated corporate bonds and low-yield western government bonds, i.e. US treasuries. So from my knowledge of only two asset-types that are virtually risk-free, you could only construct one scenario - a portfolio consisting of both US treasuries and AAA corporate bonds. Where is my knowledge lacking?

- What is the correct answer?

## Answer by user9403 (score 3)

https://quant.stackexchange.com/a/25073

Note the words "Assume" and "Scenarios". These words imply that you do not need to concern yourself with any assets that actually exist. A simple model of a market may have only one asset...clearly a vastly simplifying assumption and scenario. In this case we only have two assets. Again, this is a vastly simplifying scenario. This is a toy model which can help us understand the messiness that is real life financial markets.

Here is one of your three scenarios: you have two assets,one of which is risk free (ie, has deterministic outcome in all states of the world relative to buying power): simply buy the risk free asset and don't buy the other (presumably not risk free) asset.

## Answer by Manley (score 2)

https://quant.stackexchange.com/a/63348

Risk-free assets refer to assets with a definite rate of return and no risk of default. From the perspective of mathematical statistics, risk-free assets refer to assets with zero variance or standard deviation of investment returns. Of course, the covariance and correlation coefficient between the rate of return of risk-free assets and the rate of return of risky assets are also zero. From a theoretical point of view, only fully indexed bonds issued by the central government with a maturity matching the length of the investor’s investment period can be regarded as risk-free assets. In the real economy, there are very few securities in circulation that fully meet the above conditions. Therefore, in investment practice, risk-free assets are generally regarded as money market instruments, such as the Treasury bill interest rate LIBOR.

## Answer by ApplePie (score 1)

https://quant.stackexchange.com/a/25083

The trick to this question is that you are asked to build a risk-free portfolio, so its individual assets can be risky assets.

- Imperfect markets - If there are price inconsistencies on different markets, say market A is high and market B is low, you can build a risk-free portfolio which nets to a profit by buying a security on market B for a low price and selling to market A for a higher price.

- Perfect negative correlations - If two assets have a perfect negative correlations such that any price movement in security A is perfectly offset by price movements in security B, then a portfolio of equals parts A and B is risk-free as it is perfectly hedged.

## Answer by HyperVol (score 0)

https://quant.stackexchange.com/a/25085

Many have quoted a delta hedged option to be a risk free asset. However, I totally beg to differ here because by risk free asset , we mean a guaranteed return in future ( which is not the case with dh option). Also , a delta hedged option still has vega risk.

However, In my opinion , other than treasury , you can consider your savings bank account as a risk free asset !

## Answer by demully (score 0)

https://quant.stackexchange.com/a/63350

- Either or both assets have are "risk-free" (in the sense of zero volatility, or guaranteed short-term returns). One could then build a portfolio using it/these, ignoring risky assets.

- If the assets are perfectly correlated, or perfectly negatively correlated, AND you have confidence in their volatilities, then one could construct a zero vol portfolio hedging the two assets. Which is only as "risk-free" as one's confidence in assumed vol, and the ability to frictionlessly trade without cost or market impact etc. (to rebalance the portfolio).

- If both assets are risky but either has liquid futures (or options), then one can sell these (or short-call, long-put overlay) these to convert a synthetic risk-free asset to invest in.