Some people have questioned me **why one SBD is worth less than 1 USD in exchanges**, if one SBD can be converted into the amount of STEEM that is worth 1 USD. 

Some of them claim:
>It doesn't make sense!

Or question:
>Why would someone sell for $0.93 if you can convert it into $1.00?

There is some despair too:
>People are wasting money!

And the more enterpreneur ones believe:
>I can profit the difference from buying SBD and converting it into a dollar!

All of these people probably believe:
>It's the f***ing whales who are driving the price below $1.00 in order to profit from the difference!

(Whatever that conspiracy theory means... no idea lol)

After some days of thinking and research, I encountered and analyzed some key differences and effects that must be taken into consideration:   

- one week moving average conversion rate inflation; 
- the (uncertain) interest rate; 
- transaction costs; 
- inconvertibility (default) risk;
- technology risks.

If you consider everything, then you realize the fairest price is **not exactly $1.00**, as naively imagined. However, the good news is it is approximate and, most importantly, **quite steady**, which is **a very desirable quality** for a token.

# One week moving average conversion rate inflation 

Conversion from SBD to STEEM is executed at the future one week moving median exchange rate. So, for exemple, if 1 Steem turns out to be, in average, $0.50 for the 7 following days, 1 SBD would be converted into 2 Steem. **How can we analyze the impact of this rule on pricing?** Here, the **Arbitrage Pricing Theory (APT)** applies. As SBD can be converted at anytime to 1 USD, but the conversion is delayed in 7 days, we must consider it a **mix of spot and derivative**, with delivery set in 7 days. I will not extend myself too much here, as I have already posted something about this very impact. Please refer to https://steemit.com/steemit/@jvper/the-fair-value-of-1-sbd-steem-backed-dollar-a-thorough-financial-valuation-approach
After studying it a lot, I came to the conclusion that there is an **overall loss of nearly 3.32% in average**. 

(And earned 70 cents for all the study and time spent on it. Every cent counts when it is given with all one's heart! I didn't do it for the money anyway, so it was actually a plus, so thanks a lot for the support)

# The (uncertain) interest rate 

USD (fiat currency) can be invested into US bonds, which are generally considered risk-free assets. Fed funds rates are currently near 0% to 0.25% and are expected to be raised in the medium term, as spoken by the chairwoman Janet Yellen last Wednesday. US 5-year bond yield is around 1.286% per year. There is some volatility over this yield, which means there is some risk in the bonds prices. On the other hand, SBD has a 10% annual flat interest rate. The actual interest rate can be changed by consensus of the active miners, so there is a considerable uncertainty here. 
Forward rates usually discount such risks in what is called "price risk" of bonds. Remember that the higher the duration of a security is, the higher the variation in price will be for a specific change in the interest rate. Forward rates already carry a premium due to this risk. SBD annual rate is 10%, which is a "risky" rate, not a risk-free rate. It is usual to see a premium of nearly 10% in forward rates, which can reach 20% in stress times. In the case of SBD, the risk is much higher, therefore I am going to consider a 60% premium (6 percentage points penalty) over 5 years. This assumption may be subject to other considerations. As a result, one can either have 1.065975 USD by investing 1 USD at the US 5-year bond or buy SBD and have Steem worth 1.217 USD in 5 years (risk discounted). The difference is 14,13%. Please consider that such assumptions are very personal indeed, but these impacts surely exist to some extent.

# Transaction costs

In terms of liquidity, fiat currency is currently much more liquid. We still cannot use SBDs to buy useful things, so we need to convert it to Steem and then to bitcoin (or directly to bitcoin in Poloniex, for instance). Usually, in the end, from bitcoin to fiat currencies. There are some costs involved in these transactions. Considering we are analyzing SBD under the perspective of an investment alternative, this process occurs twice (buying SBD and selling SBD). The main costs are bid-ask spreads (around 0.4% for buying in two steps and 0.4% for selling in two steps), exchange fees (0.50% for buying in two steps and 0.50% for selling in two steps), deposit fees (0.1%) and withdraw fees (0.19%), totalling near 2.1%. These figures vary from country to country, as different exchanges charge different values. I considered the costs for an american person, using Kraken for fiat currency transactions into and out of bitcoin and Poloniex for BTC / SBD conversion. SBD to Steem was considered free of charges, or not applicable.

# Inconvertibility (default) risk

In order to model such risk, we can make use of a structural model for credit risk, like the Merton Model (1974). This model takes an overly simple debt structure, and assumes that the total value At of a firm’s assets follows a geometric Brownian motion under:  dAt = µAtdt + σAtdWt,  A0 > 0,  where:  µ is the mean rate of return on the assets;  σ is the asset volatility. 

I drew this graph in order that steemers can understand it:
![Alt text](http://i.imgur.com/CwpyYoT.png)

For more information, please refer to
https://steemit.com/steemit/@jvper/sbd-is-rating-aa-a-valuation-on-its-inconvertibility-risk

The final result is that this impact is nearly 0.1%.

# Technology Risks 
This is where it gets personal. This is the worst to calculate, as we don't have enough data. In my opinion, buying the US bond is tech risk-free, while I would discount the SBD price nearly 10% due to technology risks (hackers, password issues, DAO-style failure, etc.).

# Final result

One SBD is not really 1 USD, but, as long as the values for the assumptions are steady, the fair price of an SBD will be
steady as well. Under my assumptions, the result is 

> 0.9668*1.1413*0.979*0.999*0.9 = **$0.97**

$0.97 is a similar result to what I found under that non-arbitrage perspective, posted before at https://steemit.com/steemit/@jvper/the-fair-value-of-1-sbd-steem-backed-dollar-a-thorough-financial-valuation-approach

If the market value is under $0.97, it means that the market is weighing (on average) a bit more on risks than I am at the moment, probably technology risks or interest rate risks.

I'd appreciate if @dantheman and other guys who know everything about SBD can check this post and find out anything that could make this valuation better or more accurate. I did my best with the public information (except codes, as I am unable to read codes).